Bus statistics

Exam-2

Total Points: 100

Read carefully before starting your exam

Before you start working on any part of this exam, save the Exam_2 file as Exam_2_your full name. To submit your file, log on to this course’s blackboard site, click on Exams/ Take-home Exam tab. Then, click on Exam-2 and upload your file. Keep in mind – you can submit your file only once.

[Note: In order to receive full credits, you must show your work i.e. your Excel work.]

1. The file name Exam-2, sheet named Part 1 is kept blank. Use Part 1 sheet to answer this question. Put a box around your answer. Round your answers to 4 decimal places.

Ship collisions in the Houston Ship Channel are rare. Suppose the number of collisions are Poisson distributed, with a mean of 1.2 collisions every four months. What is the probability of having less than two collisions over a four-month period?

[10 points]

2. The file name Exam-2, sheet named Part 2 is kept blank. Use Part 2 sheet to answer this question. Put a box around your answers. For (a) and (b), round your answers to 4 decimal places.

A survey conducted for the Northwestern National Life Insurance Company revealed that 70% of American workers say job stress caused frequent health problems. Suppose a random sample of 10 American workers is selected.

a) What is the probability that more than seven of them say job stress caused frequent health problems?

b) What is the probability that exactly five say job stress caused frequent health problems?

c) What is the expected [mean] number of workers that would say job stress caused frequent health problems?

[Hint: Use binomial distribution to answer question 2]

[10 + 5 + 5 = 20 points]

3. The file name Exam-2, sheet named Part 3 is kept blank. Use Part 3 sheet to answer this question. Put a box around your answer. Round your answer to 1 decimal places.

The U.S. national average door-to-doctor wait time for patients to see a doctor is now 21.3 minutes. Suppose such wait times are normally distributed with a standard deviation of 6.7 minutes. Some patients will have to wait much longer than the mean to see the doctor. In fact, based on this information, 3% of patients still have to wait more than how many minutes to see a doctor?

[15 points]

4. The file name Exam-2, sheet named Part 4 is kept blank. Use Part 4 sheet to answer this question. Put a box around your answers. Round your answers to 4 decimal places.

According to CBS Money Watch, the average monthly household cellular phone bill is $100. Suppose monthly household cell phone bills are normally distributed with a standard deviation of $11.35.

a) What is the probability that a randomly selected monthly cell phone bill is more than $127?

b) What is the probability that a randomly selected monthly cell phone bill is between $87 and $110?

c) What is the probability that a randomly selected monthly cell phone bill is no more than $82?

[7.5 + 10+ 5 = 22.5 points]

5. The file Exam-2, sheet named Flaws, lists the discrete distribution of the number of flaws found in a porcelain cup produced by a manufacturing firm. Use these data and the associated probabilities to compute the expected number of flaws and the standard deviation of flaws.

[Note: Use Excel to calculate the expected value and the standard deviation of flaws. Show your work on Flaws sheet. Do not create a new sheet or a new workbook.]

[5 + 7.5 = 12.5 points]

6. Use Part 6 sheet to answer this question. Put a box around your answers.

A bicycle company makes two mountain bike models that each come in three colors. The following table shows the production volumes for last week:

a) Based on the relative frequency assessment​ method, what is the probability that a manufactured item is white​? [Round your answer to 4 decimal places]

b) What is the probability that a product manufactured is an XB-50 and white? [Round your answer to 4 decimal places]

c) Given that a product manufactured is FL-99, what is the probability that item is white? [Round your answer to 4 decimal places]

[2.5 + 5 + 12.5 = 20 points]

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