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.

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.

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: .

Upon substituting our given values we will get,

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.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240