The amount of money that a student at harvard university carries on his/her person is normally distributed with a mean of $25 and a standard deviation of $15. what is the probability that a randomly selected sample of 25 harvard university students will have an average amount of less than $22 on his/her person?

Question

Mathematics

Brent

5 April, 03:03

The amount of money that a student at harvard university carries on his/her person is normally distributed with a mean of $25 and a standard deviation of $15. what is the probability that a randomly selected sample of 25 harvard university students will have an average amount of less than $22 on his/her person?

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Aryn · Answer 1

Mean, m = $25

Standard deviation, s = $15

Sample size, n = 25 students

X <$22

Now,

Z = [ (X - m) * Sqrt (n) ]/s = [ (22-25) * Sqrt (25) ]/15 = - 1

From Z tables,

P (X) = P (Z = - 1) = 0.1587 = 15.87%

Therefore, probability that the selected sample has an average of less than $22 is 15.87%.