Question

The height of the galactic population of humans follows a normal distribution with mean µ = 70 inches and standard deviation σ = 2.5 inches. In order to fit in their armor, stormtroopers must be between 72 inches and 74 inches tall.

(a) What percentage of the population is eligible to be stormtroopers?

(b) Luke is taller than 75% of the population. Find the difference in his height and the height of the shortest acceptable stormtrooper. Is he actually “a little short for a stormtrooper"?

Answer 1

Please don't hesitate to give a "thumbs up " for the answer, in case you're satisfied with it.

Parameters of the normal distribution are : Mean = 70, Sigma = 2.5

I order to fit in armor: 72<X<74

a. Eligible stormtropper = ?

P(72<X<74) = P(72-70 / 2,5<Z< 74-70/2,5)

= P(.8<Z<1.6)

= .9452-.7881

= 0.1571

So, 15.71% are eligible to be a storm-troppers .

b. So, luke has height such that , P(X<= height) = .75

height - Mean / Stdev = .675

height - 70 / 2.5 = .675

height = 2.5*.675+70 = 71.69

Luke' height is 71.69 inches

The difference between Luke and the shortest stormtrooper possible is 72 - 71.69 = 0.39 inches. So that' just short of the shortest storm-trooper (who will have a height of 72 inch)

So, YES.  he actually “a little short for a stormtrooper"