Answer to Question #75078 in Statistics and Probability for Kelvin

Question

Suppose that a household generates on average of 28 pounds of garbage each month for recycling.Assume garbage generation is normally distributed with standard deviation of 2 pounds. If a household is selected at random, find the probability of that household generating
a:More than 38 pounds of garbage per month
b:Between 27 and 31 pounds of garbage per month
c:Less than 30 pounds of garbage per month

Answer 1

a. P(X>38)=P(Z>(38-28)/2)=P(Z>5)=1-P(Z<5)=2.9×10^(-7).

b. P(27<X<31)=P((27-28)/2<Z<(31-28)/2)=P(-0.5<Z<1.5)=
=P(Z<1.5)-P(Z<-0.5)=0.9332-0.3085=0.6247.

c. P(X<30)=P(Z<(30-28)/2)=P(Z<1)=0.8413.