Answer to Question #98331 in Statistics and Probability for Bob Smith

Question

The mean salary offered to students who are graduating from Coastal State University this year is $24,245, with a standard deviation of $3712. A random sample of 85 Coastal State students graduating this year has been selected. What is the probability that the mean salary offer for these 85 students is $23,500 or more?
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Answer 1

$P(\bar{X}>23500)=P(Z>\frac{23500-24245}{3712/\sqrt{85}})=P(Z>-1.8504)=\\=1-P(Z<-1.8504)=1-0.0321=0.9679.$