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
