Could -free, automatic faucets actually be housing more bacteris than the old fashioned, manual kind The concern is that decreased water flow may increase the chance that bacteria grows, because the automatic faucets are not being thoroughly flushed through. It is known that 15% of cultures from older faucets in hospital patient care areas test positive for Legionella bacteria. A recent study at Johns Hopkins Hospital found Legionella bacteria growing in 10 of cultured water samples from 20 electronic faucets aIf the probability of Legionella bacteria growing in a faucet is 0.15, what is the prob ability that in a sample of 20 faucets. 10 or more have the bacteria growing (the Johns Hopkins study provide sufficient evidence that the probability of Legionella bacteria growing in electronic faucets is greater than 15%? Explain.
Answers
Answer:
Not enough evidence to reject Null hypothesis
Step-by-step explanation:
Solution:-
- A comparative study for bacterial growth in manual and electronic faucets is made.
- It is observed that there is a higher growth in electronic faucets due to slower flow rates, i.e electronic faucets are not thoroughly flushed; hence, giving more resident time for the scaled bacteria to grow.
- It is known that 15% of cultures from older faucets were tested positive for the Legionella bacteria.
- A study at John Hopkins was conducted on a sample n = 20 electronic faucets with the probability of bacteria growing in a faucet is 0.15.
- We will conduct a hypothesis for at-least half proportion of electronic faucets have cultured bacteria.
- State the hypothesis for the proportion of electronic faucets culturing Legionella bacteria:
Null Hypothesis: P = 0.15
Alternate hypothesis: P > 0.15
- To determine the test statistics for the study conducted at John hopkins. We had a sample size of n = 20, and the probability for a bacteria to grow in a faucet is 0.15.
- Denote random variable, X: The number of electronic faucets culturing Legionella bacteria.
- Since, the probability for a bacteria to grow in a faucet is independent for each new faucet. We will assume the RV " X " to follow binomial distribution with probability of success 0.15:
X ~ Bin ( 20 , 0.15 )
- We are to determine that at-least half of the sample is subjected to the said bacteria. This is the probability of P ( X ≥ 10 ).
- The pmf for a binomially distributed random variable X is given below:
\(P ( X = r ) = n_C__r * ( p(success) )^r * ( p (fail) )^(^n^-^r^)\)
Where,
p ( success ) = 0.15
p ( fail ) = 1 - p ( success ) = 1 - 0.15 = 0.85
- Use the pmf to determine the required test statistics:
\(P ( X \geq 10 ) = 1 - P ( X \leq 9 )\\\\P ( X \geq 10 ) = 1 - [ (0.85)^2^0 + 20*(0.15)*(0.85)^1^9 + 20_C_2 (0.15)^2*(0.85)^1^8 +\\\\ 20_C_3 (0.15)^3*(0.85)^1^7 + 20_C_4 (0.15)^4*(0.85)^1^6 + 20_C_5 (0.15)^5*(0.85)^1^5+\\\\ 20_C_6 (0.15)^6*(0.85)^1^4 + 20_C_7 (0.15)^7*(0.85)^1^3 + 20_C_8 (0.15)^8*(0.85)^1^2 + \\\\ 20_C_9 (0.15)^9*(0.85)^1^1\\\\\\P ( X \geq 10 ) = 1 - [ 0.03875 + 0.13679 + 0.22933 + 0.24282 + 0.18212 + 0.10284 + \\\\ 0.04537 + 0.01601 + 0.00459 + 0.00108 ]\\\\\)
\(P ( X \geq 10 ) = 1 - [ 0.997 ] = 0.003\)
- The probability that 10 or more electronic faucets is found to have Legionella bacteria growing is 0.003
- The test proportion of 10 and more electronic faucets have culturing bacteria is p = 0.003.
- Assuming normality of the population, the Z-statistics would be:
\(Z-test = \frac{ (p - P) \sqrt{n} }{\sqrt{P*(1 - P )} } \\\\Z-test = \frac{ (0.003 - 0.15) \sqrt{20} }{\sqrt{0.15*(0.85)} } \\\\Z-test = -1.84109\)
- If we were to test the claim to 90% level of confidence:
significance level (α) = 1 - CI = 1 - 0.9 = 0.1
- The rejection region Z-critical is defined by a right-tail:
\(Z-critical \geq Z_\alpha \geq Z_0_._2\\\\Z-critical \geq 1.28\)
- Compare the test statistics with the rejection criteria defined by the Z-critical:
Z-test < Z-critical
-1.84 < 1.28
Conclusion:
There is not enough evidence that the probability of Legionella bacteria growing in electronic faucets is greater than 15%.
Related Questions
brainliest for answer
Answers
4/15 !! hope it helps loll
Explain your answer !!
Have a great day
Will give brainlst
Answers
Answer:
Dang this looks hard
Step-by-step explanation:
Wish could help
Which is a graph for the inequality m greater than or equal to 2?
Answers
Answer:
The third one is the answer. if you ever need help hit me up.
Step-by-step explanation:
John had 54 filters to post around town. Last week, he posted 1/3 of them. This week, he posted 1/6 of the remaining fliers. How many fliers has he still not posted?
Answers
Answer:
30 fliers
Step-by-step explanation:
54*1/3 = 18
subtract how many he posted=
36
1/6 of 36 is 6
subtract
36-6
30
Samuel wants to deposit $4,000 and keep that money in the bank without deposits or withdrawals for three years. He compares two different options. Option 1 will
pay 1.8% interest, compounded quarterly. Option 2 will pay 1.5% interest, compounded continuously.
How much interest does Option pay?
b. How much interest does Option 2 pay
Answers
Part (a)
The compound interest formula is
A = P*(1+r/n)^(n*t)
where,
A = account balance after t yearsP = deposit amountr = annual interest rate in decimal formn = number of times the money is compounded per yeart = number of yearsFor option 1, we have these values:
P = 4000r = 0.018n = 4t = 3Plug them into the formula to get:
A = P*(1+r/n)^(n*t)
A = 4000*(1+0.018/4)^(4*3)
A = 4221.4270078004
A = 4221.43
The account balance after three years is $4221.43
Then subtract off the deposit to find the interest made.
i = A - P
i = 4221.43 - 4000
i = 221.43
Answer: Option 1 pays $221.43 in interest.
====================================================
Part (b)
If n heads to infinity, then the compound interest formula is replaced with the continuously compounded interest formula.
That formula is
A = P*e^(r*t)
where the new item 'e' is a special constant.
e = 2.718...
It's similar to how pi = 3.14...
Most calculators have an "e" button, so it's best to let the calculator handle the decimal digits of "e".
For option 2, we have:
P = 4000r = 0.015t = 3So,
A = P*e^(r*t)
A = 4000*e^(0.015*3)
A = 4184.11143963493
A = 4184.11
and,
i = A - P
i = 4184.11 - 4000
i = 184.11
Answer: Option 2 pays $184.11 in interest.
Option 1 is the better choice.
john wants to apply for a loan, with a present annuity due value of $3,500,568.78 course herofrom a bank that charges 14.28 % interest per annum, compounded monthly. if he can only be able to pay back $43,367.21 per annum at the beginning of each year, when will john fully pay all of his debt to the bank?
Answers
The difference between what John pays and the debt increases over the years, so he will never be able to pay the loan with that annual amount.
Since John wants to apply for a loan, with a present annuity due value of $ 3,500,568.78, from a bank that charges 14.28% interest per annum, compounded monthly, if he can only be able to pay back $ 43,367.21 per annum at the beginning of each year, to determine when will John fully pay all of his debt to the bank, the following calculation must be performed:
43,367.21 x 5 = 216,836.05 3,500,568.78 x (1 + 0.1428 / 12) ^ (5x12) = 7,118,596.39 43,367.21 x 10 = 433,672.10 3,500,568.78 x (1 + 0.1428 / 12) ^ (10x12) = 14,476,051.66
Thus, as can be seen, the difference between what John pays and the debt increases over the years, so he will never be able to pay the loan with that annual amount.
Learn more about maths in https://brainly.com/question/25908673
A rectangular garden is 8 ft longer than it is wide. Its area is 425 ft2. What are its dimensions?
Answers
Answer:
17 ft.
Step-by-step explanation:
Because 17x25=425
And 25-8=17
(b) Find z such that 39% of all observations from a standard normal distribution are greater than z. (Enter your answer rounded to two decimal places.)
Answers
For 39% of all observations that are greater than z on the normal distribution table, the percentage of observations that are lesser than z is
100 - 39 = 61%
The proportion is 61/100 = 0.61
From the normal distribution table, the value of z corresponding to this proportion is 0.28
Thus, the required value of z is 0.28
Mark was working on the long jump competition, and he was able to jump 9 3/4 feet. Chris jumped 7/8 as far as Mark. write and solve the equation that will help you fight how far Chris jumped. explain the steps you took to solve problem. THIS URGENT PLEASE HELP!!
Answers
Answer:
10 5/8
Step-by-step explanation:
9 3/4 + 7/8 = 9 6/8+7/8=
10 5/8
The distance jumped by Chris in total would be as follows:
\(10\frac{5}{8}\)
Find the distance
Distance is denoted as the space that one covers from a particular place to the other.
Given that,
The distance jumped by Mark \(= 9\frac{3}{4}\) feet
The distance jumped by Chris \(= \frac{7}{8} + 9\frac{3}{4}\)
So,
The total distance covered by Chris would be:
\(= \frac{7}{8} + 9\frac{3}{4}\)
\(= \frac{7}{8} + \frac{39}{4}\)
\(=\) \(\frac{(7 + 78)}{8}\)
\(= \frac{85}{8}\)
\(=\) \(10\frac{5}{8}\)
Thus, \(10\frac{5}{8}\) is the correct answer.
Learn more about "Fraction" here:
brainly.com/question/1301963
Jim began a 145mile bicycle trip to build up stamina for a triathlon competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 7 hours. If Jim walks at a rate of 4 miles per hour and rides at 30 miles per hour, find the amount of time he spent on the bicycle.
Answers
The amount of time he spent on bicycle is 4.5 hours.
Given Jim began a 145 mile bicycle trip.
The whole trip took 7 hours.
Jim walks at a rate of 4 miles per hour and rides at 30 miles per hour.
speed = distance / time
time = distance / speed
ride:
d = distance ridden
t = d/30 (given from the problem)
walk:
t = (145 - d)/4 (given from problem)
total trip time:
7 = d/30 + (145 - d)/4.
7 = 4d/120 + 30(145 - d)/120
7×120 = 4d + 30(145 - d)
840= 4d +4350-30d
840 ₋ 4350 = ₋30d ₊ 4d
₋3510 = ₋26d
d = 3510/26
d = 135
d=135 then from here using the formula t = d / s we can solve
t=135/30 = 4.5 hours
hence the amount of time Jim spent on the bicycle is 4.5 hours.
Learn more about Speed, time and distance here:
https://brainly.com/question/17146782
#SPJ9
Nia is training for a marathon. Her average speed during training so far is 7.1 miles per hour. if she runs ar that rate for training run that is 1 hour and 24 minutes how long will nia run?
Answers
Answer:
about 10 my boy
Step-by-step explanation:
big big big
the weight of an apple is 150g, rounded to the nearest 5g. What is the lower bound of the weight of the apple?
What is the upper bound of the weight of the apple?
Answers
Answer:
1 answer
Answer:lower bound = 147.5gupper bound = 152.5gStep-by-step explanation:if you were rounding a single digit number to the nearest 5, ...
Step-by-step explanation:
I did part A, I need help with part B
Answers
between what two consecutive integers must log2(17) lie
Answers
Answer:
4 and 5
Step-by-step explanation:
For answering questions like this, it can be useful to remember a few of the powers of small integers:
2^4 = 16
2^5 = 32
Exponents and logarithmsA logarithm can be considered to be an exponent of the base.
\(\log_b(x) = a \ \Longleftrightarrow\ b^a=x\)
The ordering of powers of 2 relative to the number of interest (17) is ...
16 < 17 < 32
2⁴ < 17 < 2⁵ . . . . . . . . . . . . . . . . . . . expressed as powers of 2
log₂(2⁴) < log₂(17) < log₂(2⁵) . . . . . log₂ of the above inequality
4 < log₂(17) < 5 . . . . . . . . . . . . . . . . showing the values of the logs
Log₂(17) lies between 4 and 5.
__
Additional comment
Using the "change of base" formula, you can use a calculator to find the value of log₂(17). It shows you the value is between 4 and 5.
log₂(17) = log(17)/log(2) . . . . . . using logs to the same base
Find the value of y.
Answers
Answer:
y = \(\sqrt{55}\)
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(altitude)² = product of parts of hypotenuse
then
y² = 11 × 5 = 55 ( take square root of both sides )
y = \(\sqrt{55}\)
Need help with da question
Shelby filled a bucket with 9 3/4 gallons of water. A few minutes later, she realized only 7 3/10 gallons of water remained. How much water had leaked out of the bucket?
Answers
Answer:
2 9/20
Step-by-step explanation:
\(9\frac{3}{4}-7\frac{3}{10}\\\frac{39}{4} -\frac{73}{10}\\\frac{39x5}{4x5}-\frac{73x2}{10x2}\\\frac{195}{20}-\frac{146}{20}\\\frac{49}{20}\\2\frac{9}{20}\)
*I used an x for the multiplication symbol...there's no variable involved in this.
3 miles is the same as how many kilometers?
Hint: 1 mi≈ 1.6 km
Round your answer to the nearest tenth.
Answers
Answer: 4.8
Step-by-step explanation:
Find m/ABC.
A. 81°
B. 86°
C. 47°
D. 49.5°
99°
B
D
94%
Answers
The value of m ∠ABC=86° ,because of the cyclic quadrilaterals.
Hence, Option (B) is correct.
Since, We know that,
A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.
The opposite angles of a cyclic quadrilateral have a total of 180°.
Hence, We can formulate;
m ∠ABC + m ∠ADC = 180°
m ∠ABC + 94° = 180°
m ∠ABC = 180° - 94°
m ∠ABC = 86°
Similarly, one can find m∠DCB
m∠DAB + m∠DCB = 180°
99° + m∠DCB = 180°
m∠DCB = 180° - 99°
m∠DCB = 81°
Hence, m∠ABC = 86°
Learn more about cyclic quadrilaterals here:
brainly.com/question/14352697
#SPJ1
Maria is studying the phenomenon of pyramid power. She has read that items placed inside pyramids show amazing properties. Maria is going to see if the pyramid phenomenon will work on her young plants. She will construct an all-glass pyramid as shown.
The pyramid is regular with a square base, and all eight edges are the same length. From the possible solutions below, which amount is the closest estimate of the amount of glass Maria will need to construct her pyramid?
a) 1935 cm squared
b) 3353 cm squared
c) 5289.25 cm squared
d) 8642.5 cm squared
Answers
The solution that is the closest estimate of the amount of glass Maria will need to construct her pyramid would be =5289.25 cm squared. That is option C.
How to calculate the area of a square based pyramid?To calculate the area of a square based pyramid, the formula that should be used would be given below as follows:
\(area = {a}^{2} + 2a \sqrt{ \frac{a2}{4} } + {h}^{2} \)
Where:
a= 44cm
height= 44²-22²= 38.1cm
Area= 44²+ 2(44) × √44²/4 + 38.1²
= 1936+88 × √ 484+1452
= 2024× √1936
= 5807.61 cm².
Therefore the closest estimate to the final answer would be 5289.25 cm squared
Learn more about area here:
https://brainly.com/question/28470545
#SPJ1
Is 170 1/10 of 17? True or false?
Answers
1/10 of 17 is 1.7 and 1/10 of 1700 is 170.
A publishing company conducted a survey asking readers whether they use e readers. Of the 3000 readers surveyed, 1954 said they read books on e reader. The approximate sample proportion is? Which means that? %of the readers surveyed don’t use e readers
Answers
Approximately 34.87% of the readers surveyed don't use e-readers.
To find the approximate sample proportion of readers who use e-readers, we divide the number of readers who said they read books on e-readers (1954) by the total number of readers surveyed (3000):
Approximate sample proportion = Number of readers who use e-readers / Total number of readers surveyed
Approximate sample proportion = 1954 / 3000 ≈ 0.6513
To express this as a percentage, we multiply the sample proportion by 100:
Approximate sample proportion as a percentage = 0.6513 × 100
= 65.13%
Therefore, the approximate sample proportion of readers who use e-readers is approximately 65.13%.
This means that approximately 65.13% of the readers surveyed use e-readers.
To determine the percentage of readers who don't use e-readers, we subtract the sample proportion from 100%:
Percentage of readers who don't use e-readers = 100% - 65.13%
= 34.87%
To learn more on Percentage click:
https://brainly.com/question/24159063
#SPJ1
Factor the algebraic expression.
240q- 760u + 104i- 52b - 36i
Answers
Jasmine wants to use her savings of $1128 to buy video games and music CDs the total price of the music CDs she brought was $72 the video games cost $43 each what is the maximum number of video games that Jasmine can buy with her savings?
Answers
Answer:
set the amount of video games jasmine bought as x
43x + 72 = 1128
43x = 1056
x = 24.56 = 25
SOMEONE HELP !!! Please
Solve x² + 4x = 4 for x by completing the square.
Ox= -4
Ox=0
Ox=± √8+2
Ox=± √8-2
Answers
Answer:
x = ± \(\sqrt{8}\) - 2
Step-by-step explanation:
x² + 4x = 4
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(2)x + 4 = 4 + 4
(x + 2)² = 8 ( take square root of both sides )
x + 2 = ± \(\sqrt{8}\) ( subtract 2 from both sides )
x = ± \(\sqrt{8}\) - 2
What angle is not coterminal with -53
Answers
Answer:
I honestly don't know I'm just trying get my points up
Step-by-step explanation:
Sorry bestie
Find the
degree of the algebraic
expression:
3x^3 + 3x^2y^2 - y^2
Answers
Answer:
Degree 4
Step-by-step explanation:
Expression:
3x^3 + 3x^2y^2 - y^2
3x^3 - degree 33x^2y^2 - degree 2+2 = 4y^2 - degree 2So the expression has degree 4 as per the highest degree of the terms
Find f(-3) when f(x) = 4x-2x-7.
Answers
Answer:
-13
Step-by-step explanation:
f(x) = 4x-2x-7
when; f(x) = f(-3)
then, f(-3) = 4(-3) - 2(-3) - 7
= -12 + 6 - 7
= -19 + 6
= -13
The area of a triangular wedge is 90 square inches. The height is 18 inches.
What is the base2
Answers
Hello!
\(\large\boxed{b = 10in}\)
Formula for the area of a triangle:
A = 1/2(bh)
We are given the height and area, so we can plug those into the formula to solve for b:
90 = 1/2(18b)
Multiply both sides by 2:
180 = 18b
Divide both sides by 18:
b = 10 inches.
Answer:
10inches is equal to the base
Step-by-step explanation:
formula for finding the area of a triangle is
½bh which is half times base times height
-base is unknown, height is 18 and area is 90.
-½x*18=90
½of 18 is 9
1x*9=90
9*x=9x
therefore:9x=90
we devide both sides by the co-efficient of x which is 9
9 dividing 90 is 10.
therefore x is equal 10
You pick a marble, roll a die, and pick a card. How many outcomes are possible?
Answers
The total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.
How to determine How many outcomes are possibleTo determine the number of possible outcomes, we need to consider the number of outcomes for each event and then multiply them together.
1. Picking a marble: Let's assume there are n marbles to choose from. If there are n marbles, then the number of outcomes for this event is n.
2. Rolling a die: A standard die has 6 sides numbered 1 to 6. Therefore, the number of outcomes for this event is 6.
3. Picking a card: A standard deck of cards has 52 cards. Hence, the number of outcomes for this event is 52.
To find the total number of possible outcomes, we multiply the number of outcomes for each event together:
Total number of outcomes = (number of outcomes for picking a marble) × (number of outcomes for rolling a die) × (number of outcomes for picking a card)
Total number of outcomes = n × 6 × 52
Therefore, the total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.
Learn more about probability at https://brainly.com/question/13604758
#SPJ1
Saved
Autocracies have rules along with a court system and free press
Question 5 options:
True
False
Answers
Answer:
True
Step-by-step explanation: