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 95% of texas longhorn cattle. Show your work or explain how you got the answer.

According with the normal distribution, the ranges of horn lengths for the middle 95% of texas longhorn cattle is [ 51 inches, 69 inches ]

Step-by-step explanation:

Horn lengths of texas longhorn cattle are normally distributed

The mean horn spread: μ = 60 inches

With a standard deviation: σ = 4.5 inches

According with the normal distribution the range for the middle 95% of the values is: [ μ - 2σ, μ + 2σ ]

Replacing the given values:

[ 60 inches - 2 (4.5 inches), 60 inches + 2 (4.5 inches) ]

[ 60 inches - 9 inches, 60 inches + 9 inches ]

[ 51 inches, 69 inches ]