Respuesta :
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.
[tex]\text{The mean spread for horn lengths of Texas cattle } (\mu)=\text{60 inches}[/tex]
[tex]\text{The standard deviation for horn lengths of Texas cattle } (\sigma)=\text{4.5 inches}[/tex]
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, 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.
