Question

QUESTION 11 Provide an appropriate response. Assume that the heights of men are normally distributed with a mean of 66.6 inches and a standard deviation of 3.5 inches. If 100 men are randomly selected, find the probability that they have a mean height greater than 67.6 inches. 0 0.0021 0 0.0210 O 0.9005 O0.9979

Answer 1

Solution :

Given that ,

mean = $\mu$ = 66.6

standard deviation = $\sigma$ = 3.5

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 3.5 / $\sqrt$ 100 = 0.35

P($\bar x$ > 67.6) = 1 - P($\bar x$ < 67.6)

= 1 - P[($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (67.6 - 66.6) / 0.35]

= 1 - P(z < 2.86)

= 1 - 0.9979

= 0.0021

Probability = 0.0021