Question

2. 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 greater than 81. *

Answer 1

Population mean, = 75

Population standard deviation, = 11

Sample size, n = 36

According to Central Limit Theorem, P( < A) = P(Z < (A - )/)

= = 75

=

=

= 1.8333

P(mean score is greater than 81), P( > 81) = 1 - P( < 81)

= 1 - P(Z < (81 - 75)/1.8333)

= 1 - P(Z < 3.27)

= 1 - 0.9995

= 0.0005