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 ?.

Answers

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

Answer 2

The mean and standard deviation of the sampling distribution of the sample proportion will be 1.375 and 0.9984.

What is the mean and standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean.

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.

Then the mean is given as,

Mean = 0.275 x 5

Mean = 1.375

Then the standard deviation is given as,

Standard deviation = √[5 x 0.275 x (1 - 0.275)]

Standard deviation = √0.99687

Standard deviation = 0.9984

The mean and standard deviation of the sampling distribution of the sample proportion will be 1.375 and 0.9984.

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