Question

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

Answer 1

Answer:

No. of blue chips contain in a bag = P = 27.5 % = 0.27

No. of chips random selected at a time with replacement = n = 5

We know that the mean and standard deviation of the sampling distribution of the sample proportion  (p) is given by :-

\mu\-_pμ\-p = p

    = 0.275

\sigma_pσp = \sqrt{\frac{p (1-p)}{n} }np(1−p)

Where p= Population proportion and n = sample size.

Let p be the proportion of blue chips.

As per given , we have

p= 0.275

n= 5

= \sqrt{\frac{0.275 ( 1 - 0.275)}{5} }50.275(1−0.275)

= 0.1997