MA260 Statistical Analysis I

Directions: Be sure to save an electronic copy of your answer before submitting it to Ashworth College for grading. Unless otherwise stated, answer in complete sentences, and be sure to use correct English, spelling, and grammar. Refer to the “Assignment Format” page located on the Course Home page for specific format requirements.

**NOTE:** Show your work in the problems.

1. A recent article in the Myrtle Beach *Sun Times* reported that the mean labor cost to repair a color television is $90 with a standard deviation of $22. Monte’s TV Sales and Service completed repairs on two sets this morning. The labor cost for the first was $75 and it was $100 for the second. Compute ** z**values for each and comment on your findings.

2. The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds.

a. What is the area between 415 pounds and the mean?

b. What is the area between the mean and 395 pounds?

c. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?

3. The monthly sales of mufflers in the Richmond, VA area follow the normal distribution with a mean of 1200 and a standard deviation of 225. The manufacturer would like to establish inventory levels such that there is only a 5% chance of running out of stock. Where should the manufacturer set the inventory levels?

4. Research on new juvenile delinquents revealed that 38% of them committed another crime.

b. What is the probability that 40 or fewer of the delinquents will commit another crime?

c. What is the probability that between 30 and 40 of the delinquents will commit another crime?

5. An Air Force study indicates that the probability of a disaster such as the January 28, 1986 explosion of the space shuttle *Challenger* was 1 in 35. The *Challenger *flight was the 25th mission.

a. How many disasters would you expect in the first 25 flights?

b. Use the normal approximation to estimate the probability of at least one disaster in 25 missions.

**Grading Rubric**

*Please refer to the rubric below for the grading criteria for this assignment.*

CATEGORYExemplarySatisfactoryUnsatisfactoryUnacceptable

15 points11 points7 points3 points

The student sets up both

equations correctly and

provides the correct answer

for each.

The student sets up both

equations correctly and

provides the correct answer

for only one question.

The student sets up both

equations correctly and

provides the correct answer

for neither question.

The student sets up only

one equation correctly and

provides the correct

answer for only one

question.

15 points11 points7 points3 points

The student sets up all