Question

he mean weight of a breed of yearling cattle is 11871187 pounds. Suppose that weights of all such animals can be described by the Normal model ​N(11871187​,7878​). ​a) How many standard deviations from the mean would a steer weighing 10001000 pounds​ be? ​b) Which would be more​ unusual, a steer weighing 10001000 ​pounds, or one weighing 12501250 ​pounds? ​a) A steer weighing 10001000 pounds is nothing standard deviations below the mean.

Answer 1

Question

The mean weight of a breed of yearling cattle is 1187 pounds. Suppose that weights of all such animals can be described by the Normal model ​N(1187,78). ​

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:

a. z = -2.40

A sleet weighing 1,000 pounds is 2.40 standard deviations below the mean.

b. z = 0.81

1000 is more unusual because its contained on the extreme end from the mean

Explanation:

a.

Let weight (in pounds) of the cattle be denoted by letter x:

z = (x - u)/ σ

Where u = mean and σ = standard deviation

u = 1187

σ = 78

x = 1000

Use z score formula to standardize the value of x:

z = (1000 - 1187)/78

z = -187/78

z = -2.397436

z = -2.40 ------_ Approximated

A sleet weighing 1,000 pounds is 2.40 standard deviations below the mean.

b.

x= 1250

z= (1250 - 1187)/78

z = 63/78

z = 0.807692

z = 0.81 --------- Approximated

1000 is more unusual because its contained on the extreme end from the mean