For one quantitative coures in a college with 10,000 students, it is calculated that students test scores are normally distributed with a meanof 80 and a standard deviateion of 16. Assume now we randomly select a sample of 64 students test scores.

a.) What is the probabilitythat the average test score of the sample selected will be between 75 and 85?

b.) What is the probability that the average test score of the sample taken will be larger than 82?

c.) What is the probability that the average test score from the sample will be less than 77?

Step by step method for computing probability based on the sampling distribution of sample mean is given in the answer.