Question

Complete the following three short answer problems. If you are able, feel free to print this out and write out your answers. If you do not have access to a printer, please write out your answers on a sheet of paper. You must show All Work including probability notation, probability distribution graph sketches, and circle your final answer to receive full credit. All calculations must be made in the provided Excel file. You must show a picture of your handwritten answer sheet and Excel sheet. 1. Costco installs automobile tires on a first come first-serve basis. The total time a customer needs to wait for the installation to be completed follows the normal distribution with a mean time of 106.3 minutes and a standard deviation of 18.5 minutes. What is the probability that a randomly selected customer will wait 125 minutes for his or her tires to be installed? 2. The pH scale measures the amount of alkalinity or acidity in a liquid and ranges from 0 to 14. The ideal pH for a swimming pool is 7.2. A pH that is too high or low can cause discomfort for the swimmers, especially in the eyes. Chemicals need to be added to the water to adjust the pH to the desired level. 20 pH readings were taken at the Wilson Community Pool from different locations at 10 am this morning. The average pH reading from this sample was 6.9 with a standard deviation of 0.45. Determine if corrective action is needed at this pool to adjust the pH value, a = 0.01 3. The management of the Green Bay Packers football team would like to test the hypothesis that the average price of a ticket is less than $225 on the secondary market. A random sample of 40 customers paid an average of $207 for their ticket. Assume that the standard deviation of the price of tickets for Packers games is $43. The Green Bay Packers would like to set a = 0.01. Test this hypothesis.

Answer 1

1.

mean µ = 106.3

standard deviation σ = 18.5

= P( X > 125)

= P( (X-µ)/σ > (125 - 106.3)/18.5)

= P( z >1.0108)

= 1- P( z <1.0108)

Probability by Excel function

= 1- NORM.S.DIST(1.0108, TRUE)

= 0.1562

2. Test against Standard deviation is 0.01

Average pH reading 6.9

Standard deviation 0.45

n=20

Formula... (n-1)s^{​​​​​​2}​​​​​ /6.9² = 0.08

So correct measures needs to be taken

3.

we reject H₀ if we have enough evidence to say that tickets are cheaper in secondary market. The situation have to be evaluate with a left tail test

We have Normal Distribution

1.- Hypothesis

H₀ ⇒ μ₀ = 225

Hₐ ⇒ μₐ ≠ 225

2.-Critical values :

We find α = 0.01 and z(c) = - 2.324

3.- z(s) = ( μ - μ₀ ) /( σ/√n) ⇒ z(s) = (207 -225)/ (43/√40)

z(s) = - 18 *√40/ 43 ⇒ z(s) = -113,84/ 43

z(s) = - 2.6474

4.-Evaluation

z(s) < z(c) - 2.64 < - 1.64  

z(s) is in rejection zone we reject H₀.

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