6_2
Use the empirical rule to solve the problem.
1) The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120
mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a
systolic blood pressure that lies within 3 standard deviations of the mean?
A) 67%
B) 95.%
C) 99.7%
D) 68%
E) 99.99%
1)
2) The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120
mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a
systolic blood pressure between 96 mmHg and 144 mmHg?
A) 99.99%
B) 99.7%
C) 68%
D) 95%
E) 67%
2)
3) The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 360 hours
and a standard deviation of 5 hours. What percentage of the bulbs have lifetimes that lie within 1
standard deviation of the mean?
A) 68%
B) 95%
C) 31.74%
D) 34%
E) 84.13%
3)
4) The amount of Jennifer's monthly phone bill is normally distributed with a mean of $79 and a
standard deviation of 9. Fill in the blanks.
4)
68% of her phone bills are between $___ and $___.
A) 79, 88
B) 70, 88
C) 61, 97
D) 61, 79
5) The annual precipitation for one city is normally distributed with a mean of 390 inches and a
standard deviation of 3.2 inches. Fill in the blanks.
5)
In 95% of the years, the precipitation in this city is between ___ and ___ inches.
A) 390, 396.4
B) 380.4, 399.6
C) 380.4, 390
D) 383.6, 399.6
E) 383.6, 396.4
Select the most appropriate answer.
6) Which of the following is not true about the standard normal distribution?
A) The area under the standard normal curve to the left of z = 0 is negative.
B) The total area under the standard normal curve is 1.
C) The standard normal curve is symmetric about 0.
D) About 95% of its observations fall between -2 and 2.
E) About 68% of its observations fall between -1 and 1.
Provide an appropriate response.
7) Serum cholesterol is an important risk factor for coronary disease. The level of serum
cholesterol is approximately normally distributed with a mean of 219 mg/dL and a
standard deviation of 50 mg/dL. What is the interquartile range of the level of serum
cholesterol?
Use a table of areas to find the specified area under the standard normal curve.
8) The area that lies to the left of 1.13
A) 0.8485
B) 0.8907
C) 0.4354
D) 0.1292
1
6)
7)
E) 0.8708
8)
9) The area that lies between -1.10 and -0.36
A) 0.4951
B) 0.7763
C) 0.2239
10) The area that lies to the right of 0.59
A) 0.2190
B) 0.7224
C) 0.2224
D) 0.2237
D) 0.2776
E) -0.2237
E) 0.5552
11) The shaded area shown
A) 0.9412
B) 0.9398
10)
11)
C) 0.9699
D) 0.0602
E) 0.4699
Use a table of areas for the standard normal curve to find the required z-score.
12) Find the z-score for which the area under the standard normal curve to its left is 0.96
A) 1.03
B) 1.75
C) 1.82
D) -1.75
E) -1.38
13) Find the z-score having area 0.86 to its right under the standard normal curve.
A) 1.08
B) -1.08
C) 0.5557
D) 0.8051
12)
E) -0.5557
Provide an appropriate response.
14) Suppose that property taxes on homes in Columbus, Ohio, are approximately normal in
distribution, with a mean of $3000 and a standard deviation of $1000. The property tax for
one particular home is $3500.
a.
b.
9)
13)
14)
Find the z-score for that property tax value.
What proportion of the property taxes exceeds $3500?
15) Serum cholesterol is an important risk factor for coronary disease. The level of serum
cholesterol is approximately normally distributed with a mean of 219 mg/dL and a
standard deviation of 50 mg/dL. If serum cholesterol levels of over 250 mg/dL indicate a
high-enough risk for heart disease to warrant treatment, what is the probability that a
randomly selected person will need treatment?
15)
Find the indicated probability for the normally distributed variable.
16) In one region, the September energy consumption levels for single-family homes are found to be
normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a
randomly selected home, find the probability that the September energy consumption level is
between 1100 kWh and 1225 kWh.
A) 0.3791
B) 0.2881
C) 0.1971
D) 0.0910
E) 0.8029
17) The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a
standard deviation of $45. What is the probability that a randomly selected teacher earns more than
$525 a week?
A) 0.2823
B) 0.4354
C) 0.1003
D) 0.7823
E) 0.2177
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16)
17)
18) Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard
deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g.
What percentage of legal quarters will be rejected?
A) 2.48%
B) 1.96%
C) 3.92%
D) 0.0196%
E) 1.62%
18)
19) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of
200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a
rating that is between 200 and 275.
A) 0.9332
B) 0.5
C) 0.5668
D) 0.4332
E) 0.8664
19)
20) The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30
inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter
greater than 0.32 inches?
A) 97.72%
B) 37.45%
C) 2.28%
D) 4.56%
E) 47.72%
20)
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