an automobile owner found that 20 years ago, 73% of americans said that they would prefer to purchase an american automobile. he believes that the number differs from 73% today. he selected a random sample of 47 americans and found that 36 said that they would prefer an american automobile. can it be concluded that the percentage today differs from 73%? at
Answers
The p-value is approximately 0.27, which is greater than 0.05. Therefore, we fail to reject the null hypothesis. We do not have sufficient evidence to conclude that the percentage today differs from 73% at a 5% level of significance.
To determine whether it can be concluded that the percentage today differs from 73%, we need to perform a hypothesis test.
Let p be the true proportion of Americans who prefer to purchase an American automobile today. The null hypothesis is that p = 0.73, and the alternative hypothesis is that p is not equal to 0.73.
We can use a normal approximation to the binomial distribution because the sample size is sufficiently large (n = 47) and the success-failure condition is satisfied (at least 10 successes and failures). The test statistic is calculated as:
z = (P - p) / √(p(1-p) / n)
where P is the sample proportion, p is the hypothesized population proportion, and n is the sample size.
Plugging in the values from the problem, we have:
P = 36/47 ≈ 0.766
p = 0.73
n = 47
The calculated value of the test statistic is:
z = (0.766 - 0.73) / √(0.73(1-0.73) / 47) ≈ 1.11
Using a standard normal distribution table or a calculator, we can find the p-value associated with this test statistic. For a two-tailed test with a significance level of 0.05, the critical values are ±1.96. The rejection region is outside of this range.
The p-value is the probability of getting a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. Since the alternative hypothesis is two-sided, we need to double the area in the tail of the normal distribution that corresponds to the observed test statistic.
To know more about percentage,
https://brainly.com/question/16391559
#SPJ11
Related Questions
(Second Isomorphism Theorem) If K is a subgroup of G and N is a normal subgroup of G, prove that K/(K ∩ N) is isomorphic to KN/N
Answers
We use the First Isomorphism Theorem to show that K/(K ∩ N) is isomorphic to the image of φ, which is φ(K) = {kN | k is in K}. Since φ is a homomorphism, φ(K) is a subgroup of KN/N. Moreover, φ is onto, meaning that every element of KN/N is in the image of φ. Therefore, by the First Isomorphism Theorem, K/(K ∩ N) is isomorphic to KN/N, completing the proof of the Second Isomorphism Theorem.
To prove the Second Isomorphism Theorem, we need to show that K/(K ∩ N) is isomorphic to KN/N, where K is a subgroup of G and N is a normal subgroup of G.
First, we define a homomorphism φ: K → KN/N by φ(k) = kN, where kN is the coset of k in KN/N. We need to show that φ is well-defined, meaning that if k1 and k2 are in the same coset of K ∩ N, then φ(k1) = φ(k2). This is true because if k1 and k2 are in the same coset of K ∩ N, then k1n = k2 for some n in N. Then φ(k1) = k1N = k1nn⁻¹N = k2N = φ(k2), showing that φ is well-defined.
Next, we show that φ is a homomorphism. Let k1 and k2 be elements of K. Then φ(k1k2) = k1k2N = k1Nk2N = φ(k1)φ(k2), showing that φ is a homomorphism.
Now we show that the kernel of φ is K ∩ N. Let k be an element of K. Then φ(k) = kN = N if and only if k is in N. Therefore, k is in the kernel of φ if and only if k is in K ∩ N, showing that the kernel of φ is K ∩ N.
For such more questions on Isomorphism Theorem:
https://brainly.com/question/31227801
#SPJ11
Find || V || . v= -91 -2+ 6k IV- (Simplify your answer. Type an exact value, using fractions and radicals as needed.) Find | V || v=3i - 7j + 3k IV-(Type an exact answer, using radicals as needed.)
Answers
(a) For V = -91 - 2 + 6k, the magnitude ||V|| is an exact value, which cannot be simplified further.
(b) For V = 3i - 7j + 3k, the magnitude |V| is an exact value and can be expressed without rounding or simplification.
(a) To find the magnitude ||V|| of the vector V = -91 - 2 + 6k, we use the formula ||V|| = √(a^2 + b^2 + c^2), where a, b, and c are the components of V. In this case, a = -91, b = -2, and c = 6. Therefore:
||V|| = √((-91)^2 + (-2)^2 + (6)^2)
= √(8281 + 4 + 36)
= √8321
The magnitude ||V|| for this vector is the exact value √8321, which cannot be simplified further.
(b) For the vector V = 3i - 7j + 3k, the magnitude |V| is calculated using the same formula as above:
|V| = √(3^2 + (-7)^2 + 3^2)
= √(9 + 49 + 9)
= √67
The magnitude |V| for this vector is the exact value √67, and it does not require rounding or simplification.
In summary, the magnitude ||V|| of the vector V = -91 - 2 + 6k is √8321 (an exact value), and the magnitude |V| of the vector V = 3i - 7j + 3k is √67 (also an exact value).
To learn more about he magnitude: - brainly.com/question/28714281#SPJ11
according to the u.s. census, 67.5% of the u.s. population were born in their state of residence. in a random sample of 196 americans, what is the probability that fewer than 122 were born in their state of residence? round the final answer to at least four decimal places and intermediate z-value calculations to two decimal places.
Answers
The probability that fewer than 122 individuals from a random sample of 196 Americans were born in their state of residence is 0.0124, rounded to at least four decimal places.
Find the mean value for the binomial distribution.
Using the formula:
µ = np
where µ is the mean value, n is the sample size and p is the probability of success.
µ = np = 196 * 0.675 = 132.3
Therefore, µ = 132.3.
Find the standard deviation of the binomial distribution.
Using the formula:σ = √(np(1 - p))where σ is the standard deviation.
σ = √(np(1 - p)) = √(196 × 0.675 × (1 - 0.675))σ = √(51.975) = 7.2078
Therefore, σ = 7.2078.
Find the z-score
Using the formula:
z = (x - µ) / σ
where x is the value we want to find the probability for.z = (x - µ) / σ = (121.5 - 132.3) / 7.2078z = -1.499
Therefore, z = -1.499
Find the probability using the z-score table
Using the z-score table, the probability corresponding to a z-score of -1.499 is 0.0668.
Therefore, the probability that fewer than 122 individuals from a random sample of 196 Americans were born in their state of residence is 0.0668.
Subtracting this value from 1 gives the probability of 122 or more people being born in their state of residence.
P(≥ 122) = 1 - 0.0668 = 0.9332
Round off the final answer to at least four decimal places. P(< 122) = 0.0668, which is approximately 0.0124.
Therefore, the final probability is 0.0124.
for such more question on probability
https://brainly.com/question/24756209
#SPJ11
water leaks from a tank at a rate of 2 8t liters per hour, where t is the number of hours after 7 {\tiny{am}}. how much water is lost between 9 and 11 {\tiny{am}}?
Answers
The water that was lost between 9 and 11 am is 52 liters by using integration.
What is meant by integration?An integral in mathematics assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that come from merging infinitesimal data. The process of determining integrals is known as integration. Along with differentiation, integration is a fundamental, essential operation of calculus and is used to answer issues in mathematics and physics involving the area of an arbitrary form, the length of a curve, and the volume of a solid, among others.
The integrals listed below are definite integrals, which can be defined as the signed area of the plane region circumscribed by the graph of a given function between two points on the real line.
Rate of leaking R'(t)=2+8t
Here t is the number of hours.
Total water lost from 9 and 11 am
=\(\int\limits^8_2\) (2+8t)dt
=(2t+(8t²/2))⁴₂
=(8+64)-(4+16)
=72-20
=52 liters.
The water that was lost between 9 and 11 am is 52 liters.
To know more about integration, visit:
https://brainly.com/question/18125359
#SPJ4
on a certain standardized test, the mean is 180 and the standard deviation is 35. which of the following is within 2 standard deviations of the mean?
Answers
Any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.
Within 2 standard deviations of the mean refers to the range that includes data points within two units of standard deviation from the mean. In this case, the mean is 180 and the standard deviation is 35.
To find the range within 2 standard deviations of the mean, we need to calculate the upper and lower bounds.
The upper bound can be found by adding 2 standard deviations (2 * 35 = 70) to the mean: 180 + 70 = 250.
The lower bound can be found by subtracting 2 standard deviations (2 * 35 = 70) from the mean: 180 - 70 = 110.
Therefore, any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.
It's important to note that this answer is specific to the given mean and standard deviation. If the mean and standard deviation were different, the range within 2 standard deviations would also be different.
Always calculate the upper and lower bounds based on the provided mean and standard deviation to determine the range within 2 standard deviations accurately.
For more such questions deviations,click on
https://brainly.com/question/475676
#SPJ8
Please help will give brainiest!
Answers
Answer:
B
Step-by-step explanation:
Samuel and Joyce both bought CDs. Samuel bought 3x CDs and Joyce bought 2x-1 CDs.
¿Drive
mS
amS
Part A: If each CD had a regular price of $18 and a discount of $2, then which expression would show the amount of discount for all of their CDs?
Part B: What is the expression for the COST of their CDs, combined (ignore tax)?
Answers
Step-by-step explanation:
Part A: 3(-2) + 2(-2)
Part B: [3(8) + 2(18) - 1] - [3 + 2(-2)]
Price Discount
When two pipes fill a pool together, they can finish in 4 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours. How long will it take each pipe to fill the pool if it were working alone?
One pipe takes __ hours alone.
The other pipe takes __ hours alone.
Answers
One pipe takes 6 hours working alone.
The other pipe takes 12 hours working alone.
This is a rate of work problem. The formula utilized is
\(w=r\times t\)
where
\(w\) is the work done\(r\) is the rate of work done\(t\) is the time taken to do the workWe are looking for how long it will take each pipe to completely fill the pool
For pipe 1 working alone to fill 1 pool, the work done is 1;
\(w=r\times t\\\\1 = r_1 \times t_1\\\\t_1=\frac{1}{r_1}\)
For pipe 2 working alone to fill 1 pool, the work done is 1;
\(w=r\times t\\\\1 = r_2 \times t_2\\\\t_2=\frac{1}{r_2}\)
From the question, it would take 9 hours if each pipe took turns to fill half the pool. That is;
\(\frac{t_1}{2}+\frac{t_2}{2}=9\\\\t_1+t_2=18\)
However, if both pipes worked together, it would take 4 hours for each pipe. That is;
\(w_1+w_2=w\\\\r_1t_1+r_2t_2=w\\\\4r_1+4r_2=1\\\\r_1+r_2=\frac{1}{4}\)
Remember that \(r_1=\frac{1}{t_1}\) and \(r_2=\frac{1}{t_2}\). So,
\(\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{4}\\\\\frac{t_1+t_2}{t_1t_2}=\frac{1}{4}\)
Also recall that \(t_1+t_2=18\). So,
\(\frac{18}{t_1t_2}=\frac{1}{4}\\\\t_1t_2=72\)
The only factors of 72 that satisfy the conditions
\(t_1+t_2=18\\\\t_1t_2=72\)
are 6 and 12.
Therefore, pipe 1 will take 6 hours, and pipe 2 will take 12 hours to fill the pool if working alone.
The link below has a similar problem on rate of work
https://brainly.com/question/21485928
The product of a number, x, and six is four more than the product of the number and three-eighths.
Which answer represents this situation?
6x+38x+4
6x=38x+4
6x ⋅ 38x+4
6x=38x ⋅ 4
Answers
(b+3)(b+7) FOIL method
Answers
b^2+10b+21
Step-by-step explanation:
(b + 3)(b + 7) = ...
= b² + (3 + 7)b + (3•7)
= b² + 10b + 21
simplify (a+b)^3 + (a-b)^3 + 6a(a^2-b^2)
Answers
Answer:
8a^3.
Step-by-step explanation:
(a+b)^3=a^3+b^3+3a^2b+3ab^2
(a-b)^3=a^3-b^3-3a^2b+3ab^2
(a+b)^3+(a-b)^3=2a^3+6ab^2
According to the question
(a+b)^3+(a-b)^3+6a(a^2-b^2)
Put in the value
=2a^3+6ab^2 +6a^3–6ab^2
=8a^3
In the simplest form expression (a + b)³ + (a - b)³ + 6a(a² - b²) can be written as, 8a³
What are algebraic identities?Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.
Given that,
A algebraic identity,
(a + b)³ + (a - b)³ + 6a(a² - b²)
It is known that,
(a + b)³ = a³ + b³ + 3ab(a + b)
(a - b)³ = a³ - b³ - 3ab(a - b)
So, now we can substitute expressions
(a + b)³ + (a - b)³ + 6a(a² - b²)
a³ + b³ + 3ab(a + b) + a³ - b³ - 3ab(a - b) + 6a(a² - b²)
a³ + b³ + 3a²b + 3ab² + a³ - b³ -3a²b + 3ab² + 6a³ - 6ab²
8a³
Hence, the simplest form is 8a³
To know more about algebraic expressions check:
https://brainly.com/question/24875240
#SPJ2
27) A company promises to release a new
smartphone model every month. Each
model's battery life will be 4% longer than
the previous model's. If the current
model's battery life is 735.0 minutes, what
will the latest model's battery life be 7
months from now?
Write an exponential function, then answer the
question using that function. Show your
calculations.
Answers
Answer:
935.65 minutes.
Step-by-step explanation:
The battery life of the nth model can be represented by the exponential function:
f(n) = 735(1.04)^(n-1)
where n is the number of the model.
To find the battery life of the latest model 7 months from now, we need to find f(8):
f(8) = 735(1.04)^(8-1)
f(8) = 735(1.04)^7
f(8) = 935.65
Therefore, the battery life of the latest model 7 months from now will be approximately 935.65 minutes.
Note: The battery life is rounded to two decimal places.
(50m + 5m+20m) + 10m
Answers
Answer:
85 is the correct answer I think
The turtle's distance from his starting point is increasing
between
seconds.
The turtle's distance from his starting point is constant
between
seconds.
The turtle's distance from his starting point is
decreasing between
seconds.
Answers
Answer:
10 seconds, decreasing, standing still
Step-by-step explanation:
Price of IPAD is $750. sale price is 30% off. Tax is 5% (0.5) what is your total cost?
Answers
Answer: $262.50
Step-by-step explanation:
750x 0.5= 37.5 tax
30% of 750 is 225
225+ 37.5 is 262.50
Dan invests £13000 into his bank account. He receives 4.7% per year simple interest. How much will Dan have after 6 years? Give your answer to the nearest penny where appropriate.
Answers
Step-by-step explanation:
SI = PxTxR/100
SI= (13000)(6)(4.7)/100
SI = 366600/100
SI= 3666
can you help me? please
Answers
Answer:
The answer is B. 600
Step-by-step explanation:
Hope that helps!
Answer:
B. $600.00
Step-by-step explanation:
every 10hrs worked you are getting $120.00 so just add $120.00 every 10 hrs
5 5/7 divided by 1 3/5 times 4 2/3
Answers
Answer:
50/3
Step-by-step explanation:
5 5/7 divided by 1 3/5 times 4 2/3
5 5/7 = 40/7
1 3/5 = 8/5
4 2/3 = 14/3
40/7 divided by 8/5 = 40/7 times 5/8 = 200/56
200/56 times 14/3 = 2800/168 = 400/24 = 100/6 = 50/3
So, the answer is 50/3
An artist plans to sell $250 of prints online each week. This week, she is within $25 of her goal.
Answers
Answer:
She has $225 dollars so far.
Step-by-step explanation:
To determin the answer, its pretty simple:
take 250 and subtract 25 from 250 (250 - 25).
This would give you $225 dollars. To check, add 25 to $225 and you would get $250. $225 is your final answer.
Which sentence that is included in the text best represents the moral (lesson/purpose) of the story, "Rosie Revere, Engineer?" (hint: it's a message that represents what we believe in STEAM Enrichment as well!)
A. "But time never lingers as long as it seems"
B. "She worked and she worked till the day was half gone"
C. "The only true failure can come if you quit"
D. "After that day [Rosie] kept her dreams to herself"
Answers
Answer:
c
the only true failure can come if u quit
Which parallelogram has an area of 60 square units?
Answers
Answer:
Finding the area of each parallelogram, applying the formula, it is found that the parallelogram D has an area of 60 square units
Step-by-step explanation:
Similarly to a rectangle, the area of a parallelogram is given by height multiplied by base, that is:
In item A, the height is of 15 units and the base is of 10 units, thus, the area, in square units, is of .
In item B, the height is of 6 units and the base is of 10.2 units, thus, the area, in square units, is of .
In item C, the height is of 15 units and the base is of 15 units, thus, the area, in square units, is of .
In item D, the height is of 10 units and the base is of 6 units, thus, the area, in square units, is of , which means that this is the correct option.
PLEASE HELP I REALLY NEED HELP
Answers
Answer:
Step-by-step explanation:
To be a function you cannot have multiple inputs/or x's
Relation 1 is a function all of the domains are different
Relation 2 is a function all of the domains are different
Relation 3 is not a function, you have multiple x's, -9 and -9, that are the same
Relation 4 is not a function, you have multiple inputs that are "r"
Matt has a box that measures 23 feet long and 16 feet wide. The volume of the box is 4,416 cubic feet. What is the height of the box in yards?
Answers
Answer:
ok
Step-by-step explanation:
A store sells a 33-pound bag of oranges for \$ 3.60$3.60 and a 55-pound bag of oranges for \$ 5.25$5.25. What is the difference between the price per pound for the 33-pound bag of oranges and the price per pound for the 55-pound bag of oranges?
Answers
Answer:
0.01364
Step-by-step explanation:
It is given that,
A store sells a 33-pound bag of oranges for $3.60 and a 55-pound bag of oranges for $5.25.
Price per pound of 33 pound bag is 3.60/33 = 0.10909 price per pound
Price per pound of 55 pound bag of oranges is 5.25/55 = 0.09545 price per pound
Difference between price per pound for the 33-pound bag of oranges and the price per pound for the 55-pound bag of oranges is :
D = 0.10909 - 0.09545
D = 0.01364
Therefore, this is the required solution.
How do you find the measure of an angle in a triangle isosceles?
Answers
To find the measure of an angle in a triangle that is isosceles, you can use the fact that the two equal sides of the triangle are congruent to each other. The measure of each of these angles can be found by subtracting the measure of the third angle from 180 degrees.
Determine which two sides of the triangle are equal in length (these are called the "congruent sides").
Find the measure of the angle opposite one of the congruent sides. This angle is called the "base angle."
Subtract the measure of the base angle from 180 degrees. This will give you the measure of the other two angles in the triangle (since the three angles in any triangle must add up to 180 degrees).
For example, if the measure of the base angle is x degrees, then the measure of the other two angles would be (180-x) degrees.
To know more about triangle click below:
https://brainly.com/question/2773823#
#SPJ4
The measure of angles in an isosceles triangle can be found using the Triangle Angle Sum Theorem. This theorem states that the sum of the angles in any triangle is 180 degrees. Therefore, if you know two of the angles in the triangle, you can find the third angle by subtracting the sum of the two known angles from 180.
To find the measure of an angle in a triangle isosceles, you can use the Triangle Angle Sum Theorem. This theorem states that the sum of the angles in any triangle is 180 degrees. Therefore, if you know two of the angles in the triangle, you can find the third angle by subtracting the sum of the two known angles from 180.
Let's look at an example. Suppose you have an isosceles triangle and you know that two of its angles measure 50 degrees and 60 degrees. To find the measure of the third angle, you would subtract 110 (the sum of the two known angles) from 180. This gives you 70 degrees as the measure of the third angle.
In addition to the Triangle Angle Sum Theorem, you can also use the Isosceles Triangle Theorem to find the measure of an angle in an isosceles triangle. The Isosceles Triangle Theorem states that the angles opposite the two equal sides of an isosceles triangle are equal. This means that if you know one of the angles in the triangle, you can determine the measure of the other two angles, since they will both be equal to the measure of the known angle.
Learn more about isosceles triangle here
https://brainly.com/question/2456591
#SPJ4
PLS HELP URGENT I WILL GIVE 30 POINTS
Answers
Mrs. Sweettooth bought 2 packages of donuts (96 donuts) and 3 packages of chocolate bars (108 chocolate bars).
Let's assume Mrs. Sweettooth bought x packages of donuts and y packages of chocolate bars.
From the given information, we can set up the following equations:
Equation 1:
48x (number of donuts) + 36y (number of chocolate bars) = 204 (total donuts and chocolate bars)
Equation 2: 28x (cost of donuts) + 22.50y (cost of chocolate bars) = 123.50 (total cost)
We can solve these equations simultaneously to find the values of x and y.
Multiplying Equation 1 by 28 and Equation 2 by 48 to eliminate x, we get:
Equation 3: 1344x + 1008y = 5712
Equation 4: 1344x + 1080y = 5928
Now, subtracting Equation 3 from Equation 4, we get:
1080y - 1008y = 5928 - 5712
72y = 216
y = 216 / 72
y = 3
Substituting the value of y into Equation 3, we can solve for x:
1344x + 1008(3) = 5712
1344x + 3024 = 5712
1344x = 5712 - 3024
1344x = 2688
x = 2688 / 1344
x = 2
Therefore, Mrs. Sweettooth bought 2 packages of donuts (96 donuts) and 3 packages of chocolate bars (108 chocolate bars).
Learn more about Equation click;
https://brainly.com/question/29657983
#SPJ1
Can someone please help me? I'm confused
Answers
Answer:
±1, ±2, ±2/3, ±1/3
or
1,2,2/3,1/3,-1,-2,-2/3,-1/3
Step-by-step explanation:
Start by listing all the factors of the y intercept (in this case 2)
1,2
Then list out all the factors of the coefficent with the highest degree (3 in this case)
1,3
You're then supposed to divide all possible pairs
so all the possible zeroes are
±1, ±2, ±2/3, ±1/3
Which equations could be used to solve for the unknown lengths of △ABC? Check all that apply.
sin(45°) = StartFraction B C Over 9 EndFraction
sin(45°) = StartFraction 9 Over B C EndFraction
9 tan(45°) = AC
(AC)sin(45°) = BC
cos(45°) = StartFraction B C Over 9 EndFraction
Answers
Answer:
the first and last one apply
Step-by-step explanation:
just did it on edu
The equations that can be used to solve for the unknown lengths of △ABC is as follows
sin 45 = BC / 9
cos 45 = BC / 9
Properties of a right angle triangle:One of it angle is 90 degreesThe side and angles of the triangles can be found using trigonometric ratio. The simplest ratios are sine, cosine and tangent.The ratio are represented as follows:
sin ∅ = opposite / hypotenusecos ∅ = adjacent / hypotenusetan ∅ = opposite / adjacentThe trigonometric ratios that can be used to find unknown sides is as follows:
sin 45 = BC / 9cos 45 = BC / 9learn more on right angle triangle here: https://brainly.com/question/14771025?referrer=searchResults
Given a normal distribution with u = 100 and o= 10, complete parts (a) through (d).
a. What is the probability that X> 85? The probability that X> 85 is_____(Round to four decimal places as needed.) b. What is the probability that X<80? The probability that X < 80 is ____(Round to four decimal places as needed.) c. What is the probability that X<90 or X> 130? The probability that X<90 or X> 130 is ____ (Round to four decimal places as needed.) d. 99% of the values are between what two X-values (symmetrically distributed around the mean)? 99% of the values are greater than __ and less than _(Round to two decimal places as needed.)
Answers
To solve the given problems, we'll use the properties of the normal distribution with mean μ = 100 and standard deviation σ = 10.
a. Probability that X > 85:
To find this probability, we need to calculate the area under the normal curve to the right of 85. We can use the standard normal distribution table or a calculator to find the corresponding z-score and then use the z-table to find the probability.
First, let's calculate the z-score:
z = (X - μ) / σ
z = (85 - 100) / 10
z = -15 / 10
z = -1.5
Using the z-table or a calculator, we find that the probability of Z > -1.5 is approximately 0.9332.
Therefore, the probability that X > 85 is 0.9332 (rounded to four decimal places).
b. Probability that X < 80:
Similarly, we'll calculate the z-score for X = 80:
z = (X - μ) / σ
z = (80 - 100) / 10
z = -20 / 10
z = -2
Using the z-table or a calculator, we find that the probability of Z < -2 is approximately 0.0228.
Therefore, the probability that X < 80 is 0.0228 (rounded to four decimal places).
c. Probability that X < 90 or X > 130:
To calculate this probability, we'll find the individual probabilities of X < 90 and X > 130, and then subtract the probability of their intersection.
For X < 90:
z = (90 - 100) / 10
z = -10 / 10
z = -1
Using the z-table or a calculator, we find that the probability of Z < -1 is approximately 0.1587.
For X > 130:
z = (130 - 100) / 10
z = 30 / 10
z = 3
Using the z-table or a calculator, we find that the probability of Z > 3 is approximately 0.0013.
Since these events are mutually exclusive, we can add their probabilities:
P(X < 90 or X > 130) = P(X < 90) + P(X > 130)
P(X < 90 or X > 130) = 0.1587 + 0.0013
P(X < 90 or X > 130) = 0.1600
Therefore, the probability that X < 90 or X > 130 is 0.1600 (rounded to four decimal places).
d. 99% of the values are between what two X-values (symmetrically distributed around the mean)?
To find the two X-values, we need to find the corresponding z-scores for the cumulative probabilities of 0.005 and 0.995. These probabilities correspond to the tails beyond the 99% range.
For the left tail:
z = invNorm(0.005)
z ≈ -2.576
For the right tail:
z = invNorm(0.995)
z ≈ 2.576
Now we can find the corresponding X-values:
X1 = μ + z1 * σ
X1 = 100 + (-2.576) * 10
X1 = 100 - 25.76
X1 ≈ 74.24
X2 = μ + z2 * σ
X2 = 100 + 2.576 * 10
X2 = 100 + 25.76
X2 ≈ 125.76
Therefore, 99% of the values are greater than 74.24 and less than 125.76 (rounded to two decimal places).
To learn more about probability : brainly.com/question/31828911
#SPJ11
What is 8/9 times 212