Page 179 - Probability Demystified

168 CHAPTER 9 The Normal Distribution

The area for z ¼ 1.6 from Table 9-1 is 0.945. Subtract the area from 1.
1.00 0.945 ¼ 0.055. Hence the probability that it will take a randomly
selected student longer than 32 minutes to complete the test is 0.055 or 5.5%.

PRACTICE

1. In order to qualify for a position, an applicant must score 86 or above
on a skills test. If the test scores are normally distributed with a mean
of 80 and a standard deviation of 4, find the probability that a ran-
domly selected applicant will qualify for the position.
2. If a brisk walk at 4 miles per hour burns an average of 300 calories
per hour, find the probability that a person will burn between 260 and
290 calories if the person walks briskly for one hour. Assume the
standard deviation is 20 and the variable is approximately normally
distributed.
3. The average count for snow per year that a city receives is 40 inches.
The standard deviation is 10 inches. Find the probability that next
year the city will get less than 53 inches. Assume the variable is
normally distributed.
4. If the average systolic blood pressure is 120 and the standard devia-
tion is 10, find the probability that a randomly selected person will
have a blood pressure less than 108. Assume the variable is normally
distributed.
5. A survey found that on average adults watch 2.5 hours of television
per day. The standard deviation is 0.5 hours. Find the probability
that a randomly selected adult will watch between 2.2 and 2.8 hours
per day. Assume the variable is normally distributed.

ANSWERS

86 80 6
1. z ¼ ¼ ¼ 1:5
4 4

The required area is shown in Figure 9-17.
The area for z ¼ 1.5 is 0.933. Since we are looking for the area
greater than z ¼ 1.5, subtract the table value from 1: 1 0.933 ¼
0.067. Hence the probability is 0.067 or 6.7%.