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.

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?

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

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