Answer to Question #245141 in Statistics and Probability for Janith

Question

heights of 580 students follow a normal distribution with a mean of 1.70 m and a standard deviation of 0.15 m. Determine the number of students who have a height
greater than 1.80 m
less than 1.50 m
between 1.65 m and 1.85

Answer 1

We have the next distribution: N(1.70, 0.15). It can be simplified as 1.70 + 0.15*Z, where Z - standart normal distribution.

1) $P(1.7+0.15*Z > 1.8) = P(Z>0.67) = 0.2514$

So, there are $580*0.2514=146$ students(approximately)

2) $P(1.7+0.15*Z < 1.5) = P(Z<-1.33) = 0.0918$

So, there are $580*0.0918=53$students(approximately)

3) $P(1.65< 1.7 +0.15*Z<1.85)=P(Z<1) - P(Z<-0.33)= 0.8413 - 0.3707= 0.4706$

So, there are $580*0.4706=273$ students(approximately)