The Local Pharmacy Prides Itself on the Accuracy of the Number

The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60-count prescription.The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions.To test her theory,she randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle.She finds a sample mean of 61.35.Assume a population standard deviation of 4.45.If we want the probability of a Type I error and Type II error to be equal to .05,what is the sample size needed to make both the probability of a Type I error and the probability of a Type II error as small as possible.(Assume an alternative value of the population mean of 61. )The claim is that the tablet count is different from 60.