Answer:
b. The mean of the sampling distribution will be equal to 0.2028.
f. The sampling distribution will be approximately normal.
g. The standard deviation of the sampling distribution will be 0.0336.
Step-by-step explanation:
We use the Central Limit Theorem to solve this question.
Central Limit Theorem:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean
and standard deviation
.
The sample proportion being approximately normal means that option f. is correct.
Of 143 men, 29 said they would.
This means that ![p = \frac{29}{143} = 0.2028](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B29%7D%7B143%7D%20%3D%200.2028)
This means that option b is correct.
g. The standard deviation of the sampling distribution will be 0.0336.
Lets find the standard deviation.
Sample of 143, so ![n = 143](https://tex.z-dn.net/?f=n%20%3D%20143)
![s = \sqrt{\frac{0.2028*0.7972}{143}} = 0.0336](https://tex.z-dn.net/?f=s%20%3D%20%5Csqrt%7B%5Cfrac%7B0.2028%2A0.7972%7D%7B143%7D%7D%20%3D%200.0336)
So option g. is correct.