Q:

Assume that a national fitness study reports that 10%10% of millenials exercise daily. Suppose that a researcher surveys a random sample of 250250 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.

Accepted Solution

A:
Answer: The mean μ and standard deviation σ of the sampling distribution of X  are 25 and 4.74 respectively.Step-by-step explanation:Let X be the binomial random variable that represents the number of millenials in the sample who exercise daily.As per given , the parameters associated with x aren= 250 and p=0.10Required formula , Mean = npStandard deviation: [tex]\sqrt{np(1-p)}[/tex]Similarly , the  mean μ and standard deviation σ of the sampling distribution of X will be :-Mean =[tex]\mu= 250(0.10)=25[/tex]Standard deviation: [tex]\sigma=\sqrt{np(1-p)}[/tex][tex]=\sqrt{250(0.10)(0.90)}=4.74341649025\approx4.74[/tex]Hence, the mean μ and standard deviation σ of the sampling distribution of X  are 25 and 4.74 respectively.