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 ranges of horn lengths for the middle 99.7% of texas longhorn cattle. Show your work or explain how you got the answer.

46.5 inches to 73.5 inches

Step-by-step explanation:

In a normal distribution, the empirical rule tells us that 99.7% of the data falls within 3 standard deviations from the mean. This means up to 3 below and up to 3 above.

Each standard deviation is 4.5 inches; this makes 3 standard deviations

3 (4.5) = 13.5 inches

This means 3 standard deviations below the mean will be

60-13.5 = 46.5 inches.

This means that 3 standard deviations above the mean will be 60+13.5 = 73.5 inches.