Answer to Question #245129 in Statistics and Probability for Janith

Question

heights of A 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

Mean, $\mu$  = 1.70

Standard deviation, $\sigma$  = 0.15

 

x = 1.80

z = (x – $\mu$ )/ $\sigma$  = (1.8 – 1.7)/0.15 = 0.66667

P(x > z) = 0.2525

Number of students who have a height > 1.80 m is 0.2525 of A.

 

x = 1.50

z = (x – $\mu$ )/ $\sigma$ = (1.5 – 1.7)/0.15 = –1.33333

P(x < z) = 0.0912

Number of students who have a height < 1.50 m is 0.0912 of A

 

x = 1.65, z₁ = (1.65 – 1.7)/0.15 = –0.33333

x = 1.85, z₁ = (1.85 – 1.7)/0.15 = 1

P(z₁ < x < z₂) =  0.4719

Number of students who have a height between 1.65 and 1.85 m is 0.4719 of A.