Answer:
Probability that the sample mean would be less than 23,013 dollars is 0.2358.
Step-by-step explanation:
We are given that the mean per capita income is 23,037 dollars per annum with a variance of 149,769.
Also, a sample of 134 persons is randomly selected.
Firstly, Let = sample mean
The z-score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean per capita income = 23,037 dollars p.a.
= standard deviation =
=
= 387 dollars p.a
n = sample of persons = 134
So, probability that the sample mean would be less than 23,013 dollars is given by = P( < 23,013 dollars)
P( < 23,013) = P(
<
) = P(Z < -0.72) = 1 - P(Z
0.72)
= 1 - 0.7642 = 0.2358
The above probability is calculated using the z-score table.
<em>Therefore, probability that the sample mean would be less than 23013 dollars if a sample of 134 persons is randomly selected is 0.2358.</em>