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Suppose speeds of vehicles traveling on a highway have an unknown distribution with mean 63 and standard deviation 4 miles per hour. A sample of size n-44 is randomly taken from the population and the mean is taken. Using the Central Limit Theorem for Means, what is the standard deviation for the sample mean distribution?

Sagot :

Lublanaidn

Answer:

The standard deviation for the sample mean distribution=0.603

Step-by-step explanation:

We are given that

Mean,[tex]\mu=63[/tex]

Standard deviation,[tex]\sigma=4[/tex]

n=44

We have to find the standard deviation for the sample mean distribution using  Central Limit Theorem for Means.

Standard deviation for the sample mean distribution

[tex]\sigma_x=\frac{\sigma}{\sqrt{n}}[/tex]

Using the formula

[tex]\sigma_x=\frac{4}{\sqrt{44}}[/tex]

[tex]\sigma_x=\frac{4}{\sqrt{2\times 2\times 11}}[/tex]

[tex]\sigma_x=\frac{4}{2\sqrt{11}}[/tex]

[tex]\sigma_x=\frac{2}{\sqrt{11}}[/tex]

[tex]\sigma_x=0.603[/tex]

Hence, the standard deviation for the sample mean distribution=0.603

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