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Strike441 [17]
3 years ago
5

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.
Mathematics
1 answer:
spin [16.1K]3 years ago
8 0

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.

\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.

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