Highschool Statistics; If you guess, I report. For which sample size (n) and sample proportion (p^) can a normal curve be used to approximate the sampling distribution?

A. n=21; p^=0.6

B. n=21; p^=0.3

C. n=23; p^=0.5

D. n=23; p^=0.4

B n=21; p^=0.3

Step-by-step explanation:

The math correlates to this answer if you are using the right formula.

Answer: I make a research for this problem and My Conclusion is that you answer is B. n=21; p^=0.3

I will give you my example that I use

For example, if you take a sample of 100 teens and find 60 of them own cellphones, the sample proportion of cellphone-owning teens is

The sampling distribution of has the following properties:

Its mean, denoted by

(pronounced mu sub-p-hat), equals the population proportion, p.

Its standard error, denoted by

(say sigma sub-p-hat), equals:

(Note that because n is in the denominator, the standard error decreases as n increases.)

Due to the CLT, its shape is approximately normal, provided that the sample size is large enough. Therefore you can use the normal distribution to find approximate probabilities for

The larger the sample size (n) or the closer p is to 0.50, the closer the distribution of the sample proportion is to a normal distribution.