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 middle 99.7% of a normal distribution falls within approximately 3 standard deviations from the mean.
In this case, the mean is 60 inches, so the range of horn lengths for the middle 99.7% would be:
Mean - (3 * Standard Deviation) to Mean + (3 * Standard Deviation)
= 60 - (3 * 4.5) to 60 + (3 * 4.5)
= 60 - 13.5 to 60 + 13.5
= 46.5 to 73.5
Therefore, the correct answer is d. 46.5 in.–73.5 in.