Question 378075
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Hi
a)probability that an 18-year-old man selected at random is between 68 and 70 inches tall
 {{{z = blue(x - mu)/blue(sigma)}}}
 {{{z = blue(70 - 69)/blue(2)}}}= .5  NORMSDIST(.5)  = .6915
{{{z = blue(68 - 69)/blue(2)}}}= -.5  NORMSDIST(-.5) = .3085
P(-.5 < z > .5) = .6915 - .3085 = .3829  Or 39.29%

b)random sample of sixteen 18-year-old men is selected
test statistic = {{{z =blue (X - mu)/blue(sigma/sqrt(n))}}}
 z= 1/(2/4)  =  2  NORMSDIST(2)  = .6915 = .9773
 z = -1/(2/4)= -2  NORMSDIST(-2)  = .6915 = .0228
P(-2 < z > 2) = .9973 - .0228 = .9545  Or 95.45%