Answer:
The correct option is (A) mean = 8.5; SD = 1.129.
Step-by-step explanation:
The random variable X is defined as the number of students who are right-handed.
The proportion of the number of students who are right-handed is, p = 0.85.
The random sample is of size, n = 10.
The random variable X follows a Binomial distribution.
The mean and standard deviation of a binomial distribution can be computed as:
[tex]Mean=np\\SD=\sqrt{np(1-p)}[/tex]
Compute the mean and standard deviation of the sampling distribution of X as follows:
[tex]Mean=n\times p=10\times0.85=8.5[/tex]
[tex]SD=\sqrt{np(1-p)}=\sqrt{10\times0.85\times (1-0.85))}=\sqrt{1.275}=1.12915\approx1.129[/tex]
The mean and standard deviation of the sampling distribution of X are 8.5 and 1.129.
The correct option is (A).
