Question

A teacher gets the height of each student in his class,and it has the mean of 161 cm and a standard deviation of 10cm

Approximately what percent of these student have a height greater than 164 cm?

Answer 1

Let X be a random variable representing the height of a randomly selected student, then X ~ $N(161,10^2)$

$P(X>164)=P(N(161,10^2)>164)=P(161+10N(0,1)>164)=P(N(0,1)>0.3)=0.382$

So, approximately 100%*0.382=38.2% $\approx$ 38% os students have such height