Administrative assistants in a local university have been asked to prove their proficiency in the use ofspreadsheet software by taking a proficiency test. Historically, the mean test score has been 74 with astandard deviation of 4. A random sample of size 40 is taken from the 100 administrative assistants andasked to complete the proficiency test.

a.Calculate the expected value and the standard deviation of the sample mean.

b.What is the probability that the sample mean score is more than 75, the predetermined passing score?