The service time of the first service of a BMW is found to be normally distributed, with a mean of 70 minutes and a variance of 81 minutes.
(a) If a customer brings her BMW in for its first service, what is the probability that the car will be ready within one hour?
(b) What is the probability that the job will take more than an hour and a half?
(c) What percentage of first services will be completed between 50 and 60 minutes?
(d) The BMW dealer has a policy to give its customers a 15% discount on the cost of the first service if the service is not completed within 80 minutes. From a sample of 80 customers who brought their BMWs in for its first service, how many are likely to receive the 15% discount?
(e) If the BMW dealer wants to ensure that no more than 5% of all first services will take longer than 80 minutes, what should the mean service time be?
Note: Calculate the results using the z-table and then the appropriate Excel function (i.e. NORMDIST or NORMINV).