According to a survey by the National Center for Health Statistics, the heights of adult men in the U. S. are normally distributed with a mean of 68 inches and a standard deviation of 2.75 inches. What is the probability that adult men are at most 59 inches or at least 74 inches

0.0151 is the probability  that adult men are at most 59 inches or at least 74 inches.  

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 68 inches

Standard Deviation, σ = 2.75 inches

We are given that the distribution of heights of adult men is a bell shaped distribution that is a normal distribution.

Formula:

P(height between 59 and 74)

0.0151 is the probability  that adult men are at most 59 inches or at least 74 inches.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4