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.
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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