Answer to Question #186086 in Statistics and Probability for mya

Question

A certain tutorial center has six Math tutors namely, Aubrey,

Marlyn, Louie, Tonette, Leo, and Pat. The table at the right shows the number

of hours worked by each tutor. Suppose that 3 tutors are selected at random.

Compute the standard error of the mean of the number of hours they worked. complete solution

 

Tutors: Aubrey 15hours, Marlyn 20hrs, Louie

10hrs, Tonette 13hrs, Leo 8hrs and Pat 15hrs. Let X be the number of hours

they've worked.

Answer 1

The given data can be represent as-

Since we have to select 3 random So sampling distribution of 3 tutor is given as-

Here mean of sample mean $\bar{x}=\dfrac{\sum x}{10}=\dfrac{141.3}{10}=14.13$

Variance $\sigma^2={\dfrac{\sum(x-\bar{x})^2}{N}}=\dfrac{1880.09}{10}=188.09$

Standard Error of mean $=\sqrt{\text{variance}}=\sqrt{188.09}=13.78$