Question

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?

Answer 1

Answer:

The standard deviation for the sample mean distribution=0.603

Step-by-step explanation:

We are given that

Mean,$\mu=63$

Standard deviation,$\sigma=4$

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

$\sigma_x=\frac{\sigma}{\sqrt{n}}$

Using the formula

$\sigma_x=\frac{4}{\sqrt{44}}$

$\sigma_x=\frac{4}{\sqrt{2\times 2\times 11}}$

$\sigma_x=\frac{4}{2\sqrt{11}}$

$\sigma_x=\frac{2}{\sqrt{11}}$

$\sigma_x=0.603$

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