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5) A national caterer determined that 37% of the people who sampled their food said that it was
delicious. A random sample of 144 people is obtained from a population of 5000. The 144 people
are asked to sample the caterer's food. If p is the sample proportion saying that the food is delicious, what is the standard deviation of the sampling distribution of p?
A) 0.23
B) 0.48
C) 0.002
D) 0.04

Respuesta :

alialinoti803915
Your answer is........D) 0.04

The standard deviation of the sampling distribution is 0.04, the correct option is D.

What is Standard Deviation?

Standard deviation is the measure of dispersion of data set with respect to mean.

Sample Size = n = 144

Population Size is N = 5000

n / N > 0.05

144/5000 = 0.0288 < 0.05

There is no need to apply the finite population correction factor.

The population proportion is p = 0.37

The standard deviation of the sampling Distribution is

[tex]\rm \sigma = \sqrt {\dfrac {p(1-p)}{n}}[/tex]

[tex]\rm \sigma = \sqrt {\dfrac {0.37(1-0.37)}{144}}[/tex]

= 0.0402

= 0.04

Therefore, the standard deviation of the sampling distribution of p is 0.04.

To know more about Standard Deviation

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