Can you please help by providing the answer The distribution of heights of adult men is approximately normal with mean 69 inches andstandard deviation 2.5 inches. Use the Normal Distribution to answer the following questionsbased on the situation.a. What percent of men are taller than 74 inches? State your answer as a percent rounded to1 decimal place.0.99b. Between what two heights do the middle 95% of men fall? Round to 1 decimal place.Betweenandinchesc. What percent of men are shorter than 66.5 inches? State your answer as a percentrounded to 1 decimal place.d. Do these results agree with the Empirical Rule? Fully explain your answer.

Name: Can you please help by providing the answer The distribution of height
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Can you please help by providing the answer The distribution of heights of adult men is approximately normal with mean 69 inches andstandard deviation 2.5 inches. Use the Normal Distribution to answer the following questionsbased on the situation.a.

Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If you want remaining sub-parts to be solved, then please resubmit the whole question and specify those sub-parts you want us to solve. Given, μ=69σ=2.5 Let X denotes the heights of the adult men. Therefore, X~Nμ=69,σ=2.5 a). The Probability of men are taller then 74 inches is obtained as- PX>74=1-PX<74=1-PX-μσ<74-692.5=1-Pz<2=1-0.97725 From z-distribution table=0.02275 Therefore, the required percentage of men are taller then 74 inches is 0.02275×100=2.275% i.e. 2.3%.b). Given, Px1<z<x2=0.95 For 95% middle value z=-1.96 and z=1.96 Therefore, z=x1-μσ-1.96=x1-692.5x1=69-1.96×2.5x1=64.1 and z=x2-μσ1.96=x2-692.5x2=69+1.96×2.5x2=73.9 Between (64.1) and (73.9) the middle 95% of men fall. c). The probability of men are shorter than 66.5 inches is obtained as- PX<66.5=PX-μσ<66.5-692.5=Pz<-1=0.15866 From z-distribution table