Question

The average number of calories in a 1.5 ounce chocolate bar is 225. Suppose that the distribution of calories is *approximately* normal with a population standard deviation of 10. Find the probability that the randomly selected chocolate bar will have

(a) Less than 200 calories

(b) More than 200 calories

(c) Between 200 and 220 calories

Answer 1

µ = 225

a)

                               

                                = P(Z < -2.5)

                                = 0.0062

b) P(X > 200) = 1 - P(X < 2) = 1 - 0.0062 = 0.9938

c)

                                             

                                              = P(-2.5 < Z < -0.25)

                                              = P(Z < -0.25) - P(Z < -2.5)

                                              = 0.4013 - 0.0062

                                              = 0.3951