Question

Please Double Check answers I've recived 3 wrong answers on three diffrent questions today thank you

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 17 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 17 weeks and that the population standard deviation is 2 weeks. Suppose you would like to select a random sample of 98 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is greater than 16.8. P(X > 16.8) = (Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a sample of size n = 98 is randomly selected with a mean greater than 16.8. P(M > 16.8) = (Enter your answers as numbers accurate to 4 decimal places.)

Answer 1

Solution:

Given that,

mean =   = 17

standard deviation =   = 2

A ) P ( x > 16.8 )

= 1 - P (x < 16.8 )

= 1 - P ( x -  / ) < ( 16.8 - 17 / 2)

= 1 - P ( z < - 0.2 / 2 )

= 1 - P ( z < - 0.1)

Using z table

= 1 - 0.4602

= 0.5398

Probability = 0.5398

B ) n = 98

_M = 17

_M =  ( /n) = (2 / 98 ) = 0.2020

P ( M > 16.8 )

= 1 - P ( M < 16.8 )

= 1 - P ( M -  _M/ _M) < ( 16.8 - 17 / 0.2020)

= 1 - P ( z < - 0.2 / 0.2020 )

= 1 - P ( z < - 0.99 )

Using z table

= 1 - 0.1611

= 0.8389

Probability = 0.8389