Question

Per the Barron's report the average weeks unemployed is 21.5 (population mean) with a population standard deviation of 5 weeks and a sample of 55. In the next five questions we will be calculating the probability that the sample of 55 will provide a mean within 1 week of the population mean. What is the probability to 4 decimals for (x<20.5)?

Answer 1

Solution :

Given that ,

mean = = 21.5

standard deviation = = 5

n = 55

=   = 21.5

= / n = 5 /55 = 0.674

P( < 20.5) = P(( - ) / < (20.5 - 21.5) / 0.674)

= P(z < -1.48)

Using z table

= 0.0694