Answer:
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. The mean horn spread is 60 inches with a standard deviation of 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: [tex][\mu-3\sigma,\mu+3\sigma][/tex].
Upon substituting our given values we will get,
[tex][60\text{ inches }-3*4.5\text{ inches },60\text{ inches }+3*4.5\text{ inches }][/tex]
[tex][60\text{ inches }-13.5\text{ inches },60\text{ inches }+13.5\text{ inches }][/tex]
[tex][46.5\text{ inches },73.5\text{ inches }][/tex]
Therefore, about 99.7% of the cattle population have horn lengths between 46.5 inches and 73.5 inches and option D is the correct choice.
