Heights of men are normally distributed with a mean of 75 in and a sta

danrussekme

danrussekme

Answered question

2021-11-21

Heights of men are normally distributed with a mean of 75 in and a standard deviation of 3.5 in.
a) Find the probability of randomly selecting a man with a height of less than 72 in.
b) Find the probability of randomly selecting a man with a height of greater than 74 in.
c) Find the probability of randomly selecting a man with a height that is between 71 in. and 77 in.

Answer & Explanation

Upout1940

Upout1940

Beginner2021-11-22Added 9 answers

a) z= Data point-Mean/Standard deviation
=72753.5=33.5=0.86
Observe z=0.86 in the standard normal table. The answer is 0.1949

b) z= Data point-Mean/Standard deviation
=74753.5=13.5=0.29
Observe z=0.29 in the standard normal table and subtract the result from 1. The answer is 0.6141.

c) z1= Data point-Mean/Standard deviation
=71753.5=43.5=1.14
z2= Data point-Mean/Standard deviation
=77753.5=23.5=0.57
P(71<X<77)=P(1.14<Z<0.57)
=P(Z<0.57)P(Z<1.14)=0.71570.1271=0.5886

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