Assume that the sample is taken from a large population andthe correction factor

Question

Assume that the sample is taken from a large population andthe correction factor can be ignored. The average teacher's salary is $48,000. Suppose thatthe distribution is normal with stands deviation equal to$6,200. What is the probability that a randomly selectedteacher makes less than $38,824 a year? Give your finalanswer as a percent rounded to two decimal places. Youranswer             %. Assume that the sample is taken from a large population andthe correction factor can be ignored. The average teacher's salary is $48,000. Suppose thatthe distribution is normal with stands deviation equal to$6,200. What is the probability that a randomly selectedteacher makes less than $38,824 a year? Give your finalanswer as a percent rounded to two decimal places. Youranswer             %.

Explanation / Answer

Let X be the random variable , it gives the salary of a teacher. Then X is normally distributed and X ~N(48000 , 6200 ) If Z = ( X - 48000 ) / 6200     then Z is standard normal random variable ,   Z ~ N( 0, 1)    P[ X < 38824 ] = P [ (X - 48000) / 6200< (38824 - 48000) / 6200 ]                        = P [ Z < - 1.48 ]   = 0.0694 ..........using tables

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