Answer
a. .8508
b. .9999
c. Part a
d. Women are shorter than men.
Work Step by Step
a. We use the z-score to find:
$z=\frac{72-69.5}{2.4}=1.04$
Thus, using the table of z-scores, we find that this corresponds to a probability of $.8508$
b. We use the z-score to find:
$z=\frac{72-69.5}{2.4/\sqrt{100}}=10.42$
Thus, using the table of z-scores, we find that this corresponds to a probability of $.9999$
c. Part a is more useful, for we want to know the probability of any individual person passing under the door.
d. Women are shorter than men on average, so any door men can fit under well will accommodate women as well.
