Question

The mean per capita income is 21,604 dollars per annum with a standard deviation of 727 dollars per annum. What is the probability that the sample mean would be less than 21635 dollars if a sample of 193 persons is randomly selected?

Answer 1

0.72321

Explanation:

Given that :

Mean = 21604

Standard deviation (s) = 727

Sample size (n) = 193

P(x < 21635) :

USing the relation to obtain the standardized score (Z) :

Z = (x - m) / s/√n

Z = (21635 - 21604) / 727/√193

Z = 31 / 52.330605

Z = 0.5923875

P(Z < 0.5924) = 0.72321 (Z probability calculator)

p(Z < 0) = 0.5 ( Z probability calculator)