# Normal distribution and standard deviation discussion

**Question description**

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.

a. What is the probability that of the last 100 new juvenile delinquents put on probation, 30 or more will commit 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.

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