Question

Horn lengths of Texas longhorn cattle are normally distributed. The mean horn spread is 60 inches with a standard deviation of 4.5 inches.

Calculate the range of horn lengths for the middle 99.7% of Texas longhorn cattle.

A.
51 in.–60 in.

B.
51 in.–69 in.

C.
60 in.–73.5 in.

D.
46.5 in.–73.5 in.

Answer 1

D. 46.5 in.–73.5 in.

Step-by-step explanation:

We have been given that horn lengths of Texas longhorn cattle are normally distributed.

`\text{The mean spread for horn lengths of Texas cattle } (\mu)=\text{60 inches}`

`\text{The standard deviation for horn lengths of Texas cattle } (\sigma)=\text{4.5 inches}`

Since the empirical rule states that about 99.7% of the population lies within the 3 standard deviation. So according to normal distribution the range for the middle 99.7% of the values is:
`[\mu-3\sigma,\mu+3\sigma]`.

Upon substituting our given values we will get,

`[60\text{ inches }-3*4.5\text{ inches },60\text{ inches }+3*4.5\text{ inches }]`

`[60\text{ inches }-13.5\text{ inches },60\text{ inches }+13.5\text{ inches }]`

`[46.5\text{ inches },73.5\text{ inches }]`

Therefore, the range of horn lengths for the middle 99.7% of Texas longhorn cattle is 46.5 inches to 73.5 inches and option D is the correct choice.