Answer to Question #264285 in Statistics and Probability for belle

Question

The height of the students at a particular university is normally distributed with a mean of 63 inches and a standard deviation of 3 inches. There are 5000 students at this university. How many students have a height between 60 to 66 inches? 

Answer 1

Let X be a random variable represents the height of the students, then X ~ N(63, 3) = 63 + 3N(0,1)

$P(60<X<66)=P(60<63+3N(0,1)<66)=P(-1<N(0,1)<1)=P(N(0,1)<1)-P(N(0,1)<-1)=0.84134-0.15866=0.68268$

Among the 5000 students there will be approximately $5000*0.68268=3413.4$ students with height between 60 and 66 inches