At high school, 85% of students are right-handed. Let X – the number of students who are right-handed in a random sample of 10 students from

Question

At high school, 85% of students are right-handed. Let X – the number of students who are right-handed in a random sample of 10 students from the schools. Which one of the following statements about the mean and standard deviation of the sampling distribution of X is true?A) mean = 8.5; SD = 1.129
B) mean = 8.5; SD = 0.113
C) mean = 85; SD = 1.129
D) mean = 85; SD = 0.113
E) Neither the mean or the standard deviation can be calculated from the information given.

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Eliza 4 weeks 2021-11-10T17:12:31+00:00 1 Answer 0 views 0

Answers ( )

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    2021-11-10T17:14:24+00:00

    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:

    Mean=np\\SD=\sqrt{np(1-p)}

    Compute the mean and standard deviation of the sampling distribution of X as follows:

    Mean=n\times p=10\times0.85=8.5

    SD=\sqrt{np(1-p)}=\sqrt{10\times0.85\times (1-0.85))}=\sqrt{1.275}=1.12915\approx1.129

    The mean and standard deviation of the sampling distribution of X are 8.5 and 1.129.

    The correct option is (A).

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