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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?

Respuesta :

jushmk
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%.

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