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 ]

a

step-by-step explanation:

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11 -1> 1 -1+ a

-12 > a