Question

The average on a statistics test was 75 with a standard deviation of 11. If the test scores are normally distributed, find the probability that the mean score of 36 randomly selected students is between 72 and 81.

Answer 1

Population mean, = 75

Population standard deviation, = 11

Sample size, n = 36

According to Central Limit Theorem, the mean score, will be distributed normally as,

P( < A) = P(Z < (A - )/)

= = 75

=

=

= 1.8333

P(mean score of 36 randomly selected students is between 72 and 81) = P(72 < < 81)

= P( < 81) - P( < 72)

= P(Z < (81 - 75)/1.8333) - P(Z < (72 - 75)/1.8333)

= P(Z < 3.27) - P(Z < -1.64)

= 0.9995 - 0.0505

= 0.9490