Assume that a national fitness study reports that 5% of millenials exercise daily. Suppose that a researcher surveys a random sample of 300 millenials regarding their daily exercise habits. Assume that X is a binomial random variable that represents the number of millenials in the sample who exercise daily.Compute the mean μ and standard deviation σ of the sampling distribution of X. Report μ as a whole number and σ as a decimal precise to two decimal places.

Question
Asked Oct 26, 2019

Assume that a national fitness study reports that 5% of millenials exercise daily. Suppose that a researcher surveys a random sample of 300 millenials regarding their daily exercise habits. Assume that X is a binomial random variable that represents the number of millenials in the sample who exercise daily.

Compute the mean μ and standard deviation σ of the sampling distribution of X. Report μ as a whole number and σ as a decimal precise to two decimal places.

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Step 1

Solution: We are given that a random variable X that represents the number of millenials in the sample who exercise daily follows binomial distribution.

Also we are given that 5% of millenials exercise daily and that a researcher surveys a random sample of 300 millenials regarding their daily exercise habits.

Therefore, we have:

 

р-0.05, п %3 30ю
Х ~ Вiпотial(300,0.05)
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р-0.05, п %3 30ю Х ~ Вiпотial(300,0.05)

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Step 2

We are required to find the mean μ and standard deviation σ of the sampling distribution of X.

We know that the mean and standard deviation of binomial distribution and is given below:

 

и- пр
о- упр(1- р)
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и- пр о- упр(1- р)

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Step 3

Therefore, the mean μ and standard deviation σ o...

np 300x0.05 15
np(1p) v300x0.05x0.95 3.77
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np 300x0.05 15 np(1p) v300x0.05x0.95 3.77

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