Question

Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys 150 people. The sample mean is 23.9 hours. There is a known population standard deviation of 7.0 hours. The population distribution is assumed to be normal.

Which distribution should you use for this problem? (Round your answers to two decimal places.)

X ~ (_)(_,_)

However I have asked someone already and the answer cannot be 7, it cannot be a whole number that is why I am stuck

Answer 1

Solution :

mean = $\mu$ = 23.9

standard deviation = $\sigma$ = 7.0

n = 150

The shape of _{$\bar x$} distribution is approximately normal with,

$\mu$_{$\bar x$} = $\mu$ = 23.9

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 7.0 / $\sqrt$ 150 = 0.57

_{$\bar x$} ~ N (23.9, 0.57)