A bag contains chips of which 27.5 percent are blue. A random sample of 5 chips will be selected one at a time and with replacem

Question

1 month ago

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ent. What are the mean and standard deviation of the sampling distribution of the sample proportion of blue chips for samples of size 5 ?

1 answer:

lawyer [12.5K] · Answer 1 · 2026-03-28T17:39:26+03:00

Answer:

$\mu _{\hat{p}}= 0.275\\\\ \sigma_{\hat{p}}=0.1997$

Step-by-step explanation:

It is known that the mean and standard deviation of the sampling distribution of the sample proportion( $\hat{p}$ ) are represented as follows:-

$\mu _{\hat{p}}=p\\\\ \sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}$

, where p= Population proportion and n = sample size.

Let p denote the proportion of blue chips.

According to the information provided, we have

p= 0.275

n= 5

Thus, the mean and standard deviation of the sampling distribution of the sample proportion of blue chips for samples of size 5 will be:

$\mu _{\hat{p}}= 0.275\\\\ \sigma_{\hat{p}}=\sqrt{\dfrac{ 0.275(1- 0.275)}{5}}\\\\=0.19968725547\approx0.1997$

Therefore, you will have the mean and standard deviation for the sample proportion of blue chips for samples of size 5:

$\mu _{\hat{p}}= 0.275\\\\ \sigma_{\hat{p}}=0.1997$