Question

The average on a statistics test was 75 with a standard deviation of 11. If the...

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.

Homework Answers

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

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