Q6: All students in computer science in a local university have been asked to prove their proficiency in the use of statistical package by taking a proficiency test. The school found that the mean test score has been = 80 with a standard deviation of = 12. Assume the scores follow normal distribution.

a/What is the probability that the score of a randomly selected student is more than 95?

b/ A survey of 15 students is taken. What is the probability that the sample mean score of these students is at most 75?