The mean is 47.1 and the standard deviation is 9.5 for a population. Using the Central Limit Theorem, what is the standard deviation of the

Question

The mean is 47.1 and the standard deviation is 9.5 for a population. Using the Central Limit Theorem, what is the standard deviation of the distribution of sample means for samples of size 60

in progress 0
MichaelMet 5 years 2021-07-22T10:02:09+00:00 1 Answers 29 views 0

Answers ( )

  1. haidang
    0
    2021-07-22T10:03:44+00:00
    Reply

    Answer:

    The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

    Step-by-step explanation:

    Central Limit Theorem

    The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

    For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

    Standard deviation is 9.5 for a population.

    This means that \sigma = 9.5

    Sample of 60:

    This means that n = 60

    What is the standard deviation of the distribution of sample means for samples of size 60?

    s = \frac{\sigma}{\sqrt{n}} = \frac{9.5}{\sqrt{60}} = 1.2264

    The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )