Question

Assuming that men’s weights are normally distributed with a mean of 172 lb. and a population standard deviation of 29 lb. Find the probability that 36 randomly selected men have a mean weight of less than 167 lb.

Answer 1

Solution :

Given that ,

mean = $\mu$ = 172

standard deviation = $\sigma$ = 29

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 29 / $\sqrt$ 36 = 4.8333

P($\bar x$ < 167) = P(($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (167 - 172) /4.8333 )   

P(z < -1.03)

0.1515

Probability = 0.1515