Question

The mean weight of a breed of yearling cattle is 1138 pounds. Suppose that weights of all such animals can be described by the Normal model ​N(1138​,52​).

​a) How many standard deviations from the mean would a steer weighing 1000 pounds​ be?

​b) Which would be more​ unusual, a steer weighing 1000 ​pounds, or one weighing 1250 ​pounds?

Answer 1

Given a normal model

N(1138​,52​) ~ N( , )

Mean = = 1138

Std. deviation = = 52

a) X = 1000

Z score = ( X - ) /

Z( 1000) = (1000 - 1138 ) / 52

Z = -2.65

which means the 1000 is 2.65 standard deviations below the mean

b) X = 1250

Z score = ( X - ) /

Z(1250) = (1250 - 1138 ) / 52

z = 2.15

which means the 1250 is 2.15 standard deviations above the mean

| Z(1000) |> | Z( 1250) |

2.65 > 2.15

which makes 1000 more unusual