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.

The empirical rule says that roughly 99.7% of the population is within 3 standard deviations of the mean.

Start at the center 60 which is the mean. Add on 3 standard deviations

60 + 3*4.5 = 73.5

and subtract off 3 standard deviations from the mean

60 - 3*4.5 = 46.5

So roughly 99.7% of the population of cattle has horn lengths between 46.5 inches and 73.5 inches

Answer: Choice D. 46.5 in - 73.5 in