The Baily Hill Bicycle Shop sells mountain bikes and offers a maintenance program to its customers. The manager has found the average repair bill during the maintenance program’s first year to be $15.30 with a standard deviation of $7.00.
a. What is the probability a random sample of 40 customers will have a mean repair cost exceeding $16.00?
b. What is the probability the mean repair cost for a sample of 100 customers will be between $15.10 and $15.80?
c. The manager has decided to offer a spring special. He is aware of the mean and standard deviation for repair bills last year. Therefore, he has decided to randomly select and repair the first 50 bicycles for $14.00 each. He notes this is not even 1 standard deviation below the mean price to make such repairs. He asks your advice. Is this a risky thing to do? Based upon the probability of a repair bill being $14.00 or less, what would you recommend? Discuss.