Question

Assume that a national fitness study reports that 10% of millenials exercise daily. Suppose that a researcher surveys a random sample of 250 millenials regarding their daily exercise habits. Assume that ???? is a binomial random variable that represents the number of millenials in the sample who exercise daily. Compute the mean ???? and standard deviation ???? of the sampling distribution of ???? . Report ???? as a whole number and ???? as a decimal precise to two decimal places.

Answer 1

Question: Assume that a national fitness study reports that 5% of millenials exercise daily. Suppose that a researcher surveys a random sample of 120 millenials regarding their daily exercise habits. Assume that

Answer 2

Explanation:

Let X be the number of millenials in the sample who exercise daily

Given that X is binomial with n = 250 and p = 10% = 0.1

q =
`1-p=0.9`

As per binomial distribution rule we have

Mean of X = E(X) =
`np = 25`

Variance of X =
`npq= 22.5`

Std dev=
`√(22.5) =4.74`