Statistical Analysis I

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According to a recent Myrtle Beach Sun Times article, the average labor cost to repair a color television is $90, with a standard deviation of $22. This morning, Monte's TV Sales and Service made repairs on two televisions.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.



Answer:







The first labor cost was 0.682 standard deviations below the mean and the second labor cost was 0.455 standard deviations above the mean.





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?



Answer:



a.

Area = 0.4332



b.

Area = 0.1915



c. 0.3085

Probability = 0.3085





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?



Answer:

P(x > A) = 0.05



z = 1.6449







The manufacturer should set the inventory levels at 1570.



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?



Answer:



Normal approximation:

Mean = np = 100(0.38) = 38

Standard deviation =



a.

Probability = 0.96

b.

Probability = 0.6967



c.

Probability = 0.6567





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.



Answer:

a.

You can expect 0.71 disasters.



b. Mean = np = 25(1/35) = 0.71

Standard deviation =





































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