Answered

Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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 :

lublana

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

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.