Question

A random sample of size n = 472 is taken from a population of size N = 9,700 with mean μ = −63 and variance σ2 = 176. [You may find it useful to reference the z table.]

A-1

Is it necessary to apply the finite population correction factor?

• Yes

• No

a-2. Calculate the expected value and the standard error of the sample mean. (Negative values should be indicated by a minus sign. Round "standard error" to 2 decimal places.)

Expected Value-

Standard Error-

b. What is the probability that the sample mean is between −65 and −61? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)
Probability-

c. What is the probability that the sample mean is greater than −62? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability-

Answer 1

Answer:

Given that:

A random sample of size n = 472 is taken from a population of size N = 9,700 with mean μ = −63 and variance σ2 = 176.

We convert this to standard normal as

a-1) Is it necessary to apply the finite population correction factor?

No, There is no need to apply finite population correction factor

a-2)  Calculate the expected value and the standard error of the sample mean.

Expected value =

Standard error =

Standard error =

Standard error =  

Standard error =  

b)  What is the probability that the sample mean is between −65 and −61?

c)  What is the probability that the sample mean is greater than −62?