Question

The distribution of heights of adult men is approximately normal with mean 175 centimeters and standard deviation 6.5 centimeters.

About what percent of men are shorter than 162 centimeters? Why? Explain.                                                                        

a.  95%                         b.  68%                         c.  16%                               d.  5%                                   e.  2.5%

Answer 1

Solution :

Given that ,

mean = = 175

standard deviation = =6.5

P(x <162 ) = P(( x -) / (162 - 175) / 6.5)

= P(z <-2 )

using empirical rule

=95%

note

Using Empirical rule,

P( - 1< X < + 1) = 68%

P( - 2< X < + 2) = 95%

P( - 3< X < + 3) = 99.7%