Question

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n equals 62​, find the probability of a sample mean being less than 22.9 if mu equals 23 and sigma equals 1.33. For a sample of n equals 62​, the probability of a sample mean being less than 22.9 if mu equals 23 and sigma equals 1.33 is

Answer 1

Solution :

Given that ,

mean = $\mu$ = 23

standard deviation = $\sigma$ = 1.33

n = 62

$\mu$_{$\bar x$} = 23

$\sigma$_{$\bar x$} =$\sigma$  / $\sqrt$ n = 1.33/ $\sqrt$ 62=0.17

P($\bar x$ < 22.9) = P[($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (22.9-23) / 0.17]

= P(z < -0.59)

Using z table

= 0.2776