Answer to Question #308137 in Statistics and Probability for Arun

Question

The weight (in kgs) of the children of age group of 8 years to 10 years is normally distributed with mean as 30 kgs and Sd as 5 kgs. Find the probabilities that the weight (1) lies in between 26 kgs and 40 kgs (i) is more than 45 kgs.

Answer 1

X ~ $N(30, 5^2)$

(i) $P(26<X<40)=P(26<N(30,5^2)<40)=P(26<30+5N(0,1)<40)=P(-0.8<N(0,1)<2)=P(N(0,1)<2)-P(N(0,1)<-0.8)=0.97725-0.21186=0.71314$

(ii) $P(X>45)=P(N(30,5^2)>45)=P(30+5N(0,1)>45)=P(N(0,1)>3)=0.00135$