Answer to Question #337069 in Statistics and Probability for Jhean Rica

Question

3.)If the weights of 500 students are normally distributed with a mean of 40

kgs and a variance Of 16 kgs2,

a. determine the percentage of students with weights lower than 50 kgs.

b. How many students have weights exceeding 55 kgs.?

Answer 1

a. $P(X<50)=P(Z<\frac{50-40}{4})=P(Z<2.5)=0.9938=99.38\%.$

b. $P(X>55)=P(Z>\frac{55-40}{4})=P(Z>3.75)=0.0001.$

$N=500*0.0001=0.05\approx 0.$