Question

It is known that iq scores have a normal distribution with a mean of 100 and a standard deviation of 15.
a. a random sample of 36 students is selected. what is the probability that the sample mean iq score of these 36 students is between 95 and 110?
b. a random sample of 100 students is selected. what is the probability that the sample mean iq score of these 100 students is between 95 and 110?

Answer 1

The standard deviation of the mean of the sample is the population standard deviation divided by the square root of the sample size. A suitable calculator can figure the rest for you.

a. 0.99722
b. 0.99957