Question

Assume that the salaries of computer programmers are normally distributed, with a mean of $66,000 and a standard deviation of $14,000.

If four programmers are selected at random, find the probability that they have a mean salary between $40,000 and $50,000.

a) 0.52
b) 0.09
c) 0.26
d) 0.01

Answer 1

The probability that they have a mean salary between $40,000 and $50,000 is 0.01.

What is Z- score test?

A z-test is a statistical test to determine whether two population means are different when the variances are known and the sample size is large.

The z-score for 40,000 is

= (40,000 - 66000) / (14,000 / √4)

= -26000/7000

= -3.714, P- value is 0.000102

The z-score for 50,000

= (50,000 - 66,000) / (14,000 / √4)

=-2.285, P- value is 0.0111564

P(40,000 < x < 50,000) = P(  -3.714< z < -2.285)

So,

= P(50,000)-P(40,000)

= 0.0111564-0.000102

=0.011

Hence, the probability that they have a mean salary between $40,000 and $50,000 is 0.01.

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