Answer:
n = 50
A) show the sampling distribution of x, the sample mean average for a sample of 50 unemployment individuals.
We will use central limit theorem
So, mean of sampling distribution =
Standard deviation of sampling distribution =
B) What is the probability that a simple random sample of 50 unemployment individuals will provide a sample mean within one week of the population mean?
A sample mean within one week of the population mean means
So,
=
=
=
=0.9616-0.0384
=0.9232
The probability that a simple random sample of 50 unemployment individuals will provide a sample mean within one week of the population mean is 0.9232.
C) What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within a half week of the population mean?
A sample mean within one week of the population mean means
So,
=
=
=
=0.8106-0.1894
=0.6212
The probability that a simple random sample of 50 unemployed individuals will provide a sample mean within a half week of the population mean is 0.6212