One truck from lakeland trucking inc can carry a load of 5068.8 lb. Records show that the weights of boxes that it carries have a mean of 75

Question

One truck from lakeland trucking inc can carry a load of 5068.8 lb. Records show that the weights of boxes that it carries have a mean of 75 lb and a standard deviation of 16 lb. For sample size of 64, find the mean and standard deviation of x bar.

a) mean x(bar) =2, standard deviation of x(bar) = 75
b) 16, 75
c) 75, 2
d) 75, 16

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Melanie 5 days 2021-09-13T11:36:52+00:00 1 Answer 0

Answers ( )

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    2021-09-13T11:38:04+00:00

    Answer:

    c) 75, 2

    Step-by-step explanation:

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

    In this problem, we have that:

    Records show that the weights of boxes that it carries have a mean of 75 lb and a standard deviation of 16 lb. This means that \mu = 75, \sigma = 16.

    For sample size of 64, find the mean and standard deviation of x bar

    We have that \mu = 75, s = \frac{16}{\sqrt{64}} = 2.

    So the correct answer is:

    c) 75, 2

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