4 years ago

Read the picture. The question is on number 1.

Mathematics

1 answer:

olasank [31]4 years ago

5 0

[Person] is domain (x), [Birthday] is range (y)

(Elvis, Jan. 8)

(Colleen, Jan. 8)

(Kaleigh, Mar. 15)

(Marissa, Sept. 17)

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Horn lengths of Texas longhorn cattle are normally distributed. The mean horn spread is 60 inches with a standard deviation of 4

spin [16.1K]

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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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