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 are
n= 250 and p=0.10
Required formula ,
Mean = np
Standard 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.
