Question

Hereford cattle are one of the most popular breeds of beef cattle. Based on data from the Hereford Cattle Society, the mean weight of a one-year-old Hereford bull is 1150 pounds, with a standard deviation of 80 pounds.

a. What is the probability that if a single Hereford bull is selected at random, it will weigh less than 1100 pounds? b. What weights will define the middle 50% of Hereford weights?

Answer 1

Let x be a random variable representing the mean weight of a one-year-old Hereford bull. Then
a.) P(x < 1100) = P (z < (X - mean)/sd) = P(z < (1100 - 1150)/80) = P(z < -0.625) = 1 - P(z < 0.625) = 1 - 0.73401 = 0.2660

b.) The middle (50%) of Hereford weights will weigh the mean weight of the sample. i.e. the middle (50%) of the Hereford weights will be 1150 pounds