Answer to Question #341620 in Statistics and Probability for Japp

Question

If the weights of 600 students are normally distributed with mean of 50 kilograms and a variance of 16kilograms.

a.) Determine the percentage of students with weights lower than 55 kgs.

b.) How many students with weight between 50kgs and 55kgs.

Answer 1

Let $X=$ the weight of student: $X\sim N(\mu, \sigma^2).$

Given $\mu=50kg, \sigma=\sqrt{16}kg$

a)

$$P(X<55)=P(Z<\dfrac{55-50}{\sqrt{16}})$$

$$=P(Z<1.25)=0.89435$$

$$0.89435(600)=537$$

537 students

b)

$$P(50<X<55)=P(Z<\dfrac{55-50}{\sqrt{16}})$$

$$-P(Z\le\dfrac{50-50}{\sqrt{16}})=P(Z<1.25)-P(Z\le 0)$$

$$=0.89435-0.5=0.39435$$

$$0.39435(600)=237$$

237 students