If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 204 feet

Complete question is;

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 244 feet and a standard deviation of 44 feet. Let X = distance in feet for a fly ball.

If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 184 feet? (Round your answer to four decimal places.)

0.1814

Step-by-step explanation:

We are given;

Mean; μ = 244

Standard deviation; σ = 44

Test score; x' = 204

z-score = (x' - μ)/σ

z = (204 - 244)/44

z = -0.91

Thus, probability that X travelled fewer than 184 ft is;

P(X < 184) = P(Z = -0.91)

From z-distribution table attached, P = 0.18141

Thus; P(X < 184) ≈ 0.1814

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