Question

The mean salary offered to students who are graduating from Coastal State University this year is $24,260, with a standard deviation of $3712. A random sample of 80 Coastal State students graduating this year has been selected. What is the probability that the mean salary offer for these 80 students is $24,000 or less?

Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Answer 1

Let X be the random variable denoting the salary offered to students graduated from Coastal State University.

Thus, X ~ N(24260, 3712) i.e. (X - 24260)/3712 ~ N(0, 1).

Let M be the sample mean of salary of 80 students.

Thus, E(M) = 24260, s.d.(M) = 3712/ = 415.0142.

Hence, M ~ N(24260, 415.0142) i.e. (M - 24260)/415.0142 ~ N(0,1).

The probability that mean salary is less than $24,000 or less = P(M < 24000) = P[(M - 24260)/415.0142 < (24000 - 24260)/415.0142] = P[(M - 24260)/415.0142 < - 0.6265] = (-0.6265) = 0.2655. (Ans).