Answer :
The distribution of height of men is approximately normal with mean μ = 69.2 inches and standard deviation of σ =2.5 inches.
A) According to the empirical rule of probability, about 95% observations falls within two standard deviation of mean.
Therefore,
Lower bound=μ+2*sigma
=69.2+2*2.5
=69.2+5.0
Lower bound=74.2
Upper bound=μ-2*sigma
=69.2-2*2.5
=69.2-5
Upper bound=64.2
B) The distribution of the heights of young men is approximately normal with mean mu=69.2 inches and standard deviation of sigma=2.5
The standard score of height of 72 inches is given by:
z=(72-69.2)/2.5
z=2.8/2.5
z=1.12
Hence, the distribution of height of men is approximately normal with mean μ = 69.2 inches and standard deviation of σ =2.5 inches.
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