Question

weight of a breed of yearling cattle is 1146 pounds. Suppose that weights of all such animals can be described by the Normal model N(1146,90). standard deviations from the mean d be more unusual, a steer weighing 1000 pounds, or one weighing 1250 pounds? a) How many would a steer weighing 1000 pounds t e? a) A steer weighing 1000 pounds is standard deviations below the mean Round to two decimal places as needed.) b) The steer weighing pounds is more unusual.

Answer 1

Mean weight = 1146 pounds

Standard deviation of weights = 90 pounds

Z score = (X - mean)/standard deviation

a) Z score corresponding to 1000 = (1000 - 1146)/90

= -1.62

A steer weighing 1000 pounds is 1.62 standard deviations below the mean.

b) Z score corresponding to 1250 = (1250 - 1146)/90

= 1.15

A steer weighing 1000 pounds is 1.62 standard deviations below the mean and a steer weighing 1250 pounds is 1.15 standard deviations above the mean. 1000 is farther from the mean.

The steer weighing 1000 pounds is more unusual