Question

The distribution of heights of adult men is approximately normal with mean 69 inches and standard deviation of 2.5 inches.  

a. What percent of men are shorter than 66 inches?

b. The distribution of heights of adult men is approximately normal with mean 69 inches and standard deviation of 2.5 inches. What is the probability that a man is taller than 74 inches?

c.. What is the probability that a man is between 70 and 72 inches tall?

Answer 1

Given,

Mean () = 69

Standard deviation () = 2.5

(a) So here, we have to find P( X<66)

For X=66

Z = ( X - ) /

= (66 - 69)/ 2.5

= -1.2

Now using the left tailed Z-table

We get, P(Z < -1.2) = 0.1151

So, Percent of men shorter than 66 inches = 11.51%

(b) Similarly as done in part a,

For X = 74

Z = (74 - 69)/ 2.5

= 2

So we have to find P(Z > 2)

Using right tailed Z-table we get

P(Z > 2) = 0.0228

So, the probability that a man is taller than 74 inches = 0.0228

(c). Now Similarly,

For X = 70

Z = (70 - 69) / 2.5

= 0.4

And For X = 72

Z = (72 - 69) / 2.5

= 1.2

So Now, P(0.4 < Z < 1.2) = 0.2295

So, Probability that a man is between 70 and 72 inches tall = 0.2295

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