Question

Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place if necessary

Answer 1

Given;

`\begin{gathered} \mu=59 \\ \sigma=10 \\ n=36 \end{gathered}`

To find the standard deviation of the sampling distribution of the sample mean, the formula is

`Standard\text{ deviation }\bar{X}=(\sigma)/(√(n))`

Substituting the values of the variables

`\begin{gathered} Standard\text{ dev}\imaginaryI\text{at}\imaginaryI\text{on }\bar{X}=(\sigma)/(√(n)) \\ Standard\text{ dev}\mathrm{i}\text{at}\mathrm{i}\text{on }\bar{X}=(10)/(√(36))=(10)/(6)=1.66666 \\ Standard\text{ deviation }\bar{X}=1.7\text{ \lparen one decimal place\rparen} \end{gathered}`

Hence, the answer is 1.7 (one decimal place)