Respuesta :
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 [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex].
The sample proportion being approximately normal means that option f. is correct.
Of 143 men, 29 said they would.
This means that [tex]p = \frac{29}{143} = 0.2028[/tex]
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 [tex]n = 143[/tex]
[tex]s = \sqrt{\frac{0.2028*0.7972}{143}} = 0.0336[/tex]
So option g. is correct.
The statements that accurately describe the sampling distribution of the sample proportion of men would return money from a found wallet are;
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.
Central Limit Theorem.
We are given the true proportion of all adult men who will return the money as; p = 18% = 0.18
Thus, the population mean = 0.18
Now, out of 143 men, 29 said they will return the money. Thus;
Sample mean = Sample proportion = 29/143 = 0.2028
The formula for the sampling standard deviation is;
s = √[p^(1 - p^)/n]
s = √[0.2028(1 - 0.2028)/143]
s = √0.001130574545
s = 0.0336
Looking at the options and comparing to the answers gotten above, only option B, F and G are correct.
Read more about Central Limit Theorem at; https://brainly.com/question/25800303
