Question

1. Suppose that I am looking at a sample of 30 students coming into the university. The individual scores, X, on the college entrance examination are normally distributed with a mean of 550 and a standard deviation of 100.  

a. Suppose the mean of those 30 students is 575. What is the percentile score of that mean?

b. What is the probability that the mean will be at least 600 for a set of 30 students?

Answer 1

µ = 550

sd = 100

n = 30

a)

                               

                                = P(Z < 1.37)

                                = 0.9147

                                = 91.47 percentile

b)

                              

                                = P(Z > 2.74)

                                = 1 - P(Z < 2.74)

                                = 1 - 0.9969

                                = 0.0031