  # 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

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.

check_circleExpert Solution
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:

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:

Step 3

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

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