example: What proportion of the area under a normal curve lies between z = –1.2 and z = 0.58?
solution: (i) Reading from Table A, the area to the left of z = –1.2 is 0.1151, and the area to the
left of z = 0.58 is 0.7190. The geometry of the situation (see below) tells us that the area
between the two values is 0.7190 – 0.1151 = 0.6039.(ii) Using the calculator, we have normalcdf(-1.2, 0.58) = 0.603973005. Round to 0.6040
(difference from the answer in part (i) caused by rounding).
example: In an earlier example, we saw that heights of men are approximately normally
distributed with a mean of 70 and a standard deviation of 3. What proportion of men are more
than 6′ (72′′¢) tall? Be sure to include a sketch of the situation.
solution: (i) Another way to state this is to ask what proportion of terms in a normal distribution
with mean 70 and standard deviation 3 are greater than 72. In order to use the table of Standard
Normal Probabilities, we must first convert to z -scores. The z -score corresponding to a height
of 72′′ isThe area to the left of z = 0.67 is 0.7486. However, we want the area to the right of 0.67, and that is 1 –
0.7486 = 0.2514.