Question

The mean per capita income is 17,145dollars per annum with a standard deviation of 505 dollars per annum. What is the probability that the sample mean would differ from the true mean by greater than 40 dollars if a sample of 466 persons is randomly selected? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 17145

standard deviation = = 505

= / n = 505 / 466 = 23.3937

= 1 - P[(-40) /23.3937 < ( - ) / < (40) / 23.3937)]

= 1 - P(-1.71 < Z < 1.71)

= 1 - P(Z < 1.71) - P(Z < -1.71)

= 1 - P(0.9564 - 0.0436)  

= 1 - 0.9128

= 0.0872

Probability = 0.0872