Question

A supervisor finds the mean number of miles that the employees in a department live from work. He finds x=29 and s=3.6 . Which statement must be true?

z37 is within 1 standard deviation of the mean.
z37 is between 1 and 2 standard deviations of the mean.
z37 is between 2 and 3 standard deviations of the mean.
z37 is more than 3 standard deviations of the mean.

Answer 1

C.

Explanation:

Answer 2

Option 3 is right

z37 is between 2 and 3 standard deviations of the mean.

Explanation:

Let X be a random variable which represents the mean number of miles that the employees in a department live from work

X is normal (N(29,3.6)

WE have to find Z score for X

Z =
`(x-29)/(3.6)`

=2.22

i.e. 37 is 2.22 std deviations from the mean.

In other words, z37 is between 2 and 3 standard deviations of the mean.