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STA 2023 – Test #3 Practice
Name _______________________
1. In one region, the September energy consumption levels for single-family homes are bound to be normally
distributed with a mean of 1,050 kWh and a standard deviation of 218 kWh. Find P45, which is the
consumption level separating the bottom 45% from the top 55%. Round to the nearest tenth.
2. Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are
normally distributed with a mean of 100 and a standard deviation of 15.
3. The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard
deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less
than 32 oz? Round your answer to four decimal places.
4. The lengths of pregnancies are normally distributed with a mean of 270 days and a standard deviation of 15
days.
a. Find the probability of a pregnancy lasting 309 days or longer.
b. If the length of pregnancy is in the lowest 4%, then the baby is premature. Find the length that
separates premature babies from those who are not premature.
5. Determine whether the random variable is discrete or continuous.
a.
b.
c.
d.
e.
Is the number of free-throw attempts before the first shot is made discrete or continuous?
Is the number of people in a restaurant that has a capacity of 150 discrete or continuous?
Is the exact time it takes to evaluate 27 + 72 discrete or continuous?
Is the square footage of a house discrete or continuous?
Is the number of points scored during a basketball game discrete or continuous?
6. A TV show, Lindsay and Tobias, recently had a share of 25, meaning that among the TV sets in use, 25% were
tuned to that show. Assume that an advertiser wants to verify that 25% share value by conducting its own
survey, and a pilot survey begins with 16 households having TV sets in use at the time of a Lindsay and Tobias
broadcast.
a.
b.
c.
d.
Find the probability that none of the households are tuned to Lindsay and Tobias.
Find the probability that at least one household is tuned to Lindsay and Tobias.
Find the probability that at most one household is tuned to Lindsay and Tobias.
If at most one household is tuned to Lindsay and Tobias, does it appear that the 25% share value is
wrong? Why or why not?
7. Assume that the readings on the thermometers are normally distributed with a mean of 0 and a standard
deviation of 1.00C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature
reading corresponding to P83, the 83rd percentile. This is the temperature reading separating the bottom 83%
from the top 17%.
STA 2023 – Test #3 Practice
Name _______________________
8. If z is a standard normal variable, find the probability. Round your answer to four decimal places.
P(z>0.59)
9. A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly.
If a student guesses on each question, what is the probability that the student will pass the test? Round to three
decimal places.
10. A brand name has a 60% recognition rate. If the owner of the brand wants to verify that rate by beginning with
a small sample of 10 randomly selected consumers, find the probability that exactly 6 of the 10 consumers
recognize the brand name. Also find the probability that the number who recognized the brand name is not 6.
11. Assume that the readings on the thermometers are normally distributed with a mean of 0 and a standard
deviation of 1.00C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and
find the probability of the reading. (The given values are in Celsius degrees.)
Between 1.50 and 2.25
12. Assume that X has a normal distribution. The mean is =60.0 and the standard deviation is =4.0. Find the
probability that X is less than 53.0.
13. Find the mean of the given probability
distribution. The random variable x is the number
of houses sold by a realtor in a single month at the
Sendsom’s Real Estate office.
Houses Sold (x)
0
1
2
3
4
5
6
7
Probability P(x)
0.24
0.01
0.12
0.16
0.01
0.14
0.11
0.21
14. Suppose that 14% of people are left handed. If 6 people are selected at random, what is the probability that
exactly 2 of them are left handed? Round to three decimal places.
15. An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing
between 140 lb and 181 lb. The new population of pilots has normally distributed weights with a mean of 149 lb
and a standard deviation of 29.5 lb.
a. If a pilot is randomly selected, find the probability that his weight is between 140 lb and 181 lb.
b. If 31 different pilots are randomly selected, find the probability that their mean weight is between 140
lb and 181 lb.
c. When redesigning the ejection seat, which probability is more relevant?
16. Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2
standard deviations. That is, unusual values are either less than  - 2 or greater than  + 2.
STA 2023 – Test #3 Practice
Name _______________________
A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer
Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it
be unusual to get 576 consumers who recognize the Dull Computer Company name?
17. Based on a survey, for women aged 18 to 24, systolic blood pressures (in mm Hg) are normally distributed with a
mean of 114.9 and a standard deviation of 13.1. Complete parts (a) through (d).
a. If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic
blood pressure is greater than 110.
b. If 3 women in that age bracket are randomly selected, find the probability that their mean systolic blood
pressure is greater than 110.
c. Given that part (b) involves a sample size that is not larger than 30, why can the central limit theorem be
used?
a) When the original population is normally distributed, the central limit theorem can only be
used if the sample size is less than or equal to 30.
b) Since the original population is normally distributed, the sampling distribution of sample
means will be normally distributed for any sample size.
c) The central limit theorem can always be used regardless of sample size.
d) Since the 3 women are randomly selected, the sampling distribution of sample means will be
normally distributed for any sample size.
d. If a physician is given a report stating that 3 women have a mean systolic blood pressure below 110, can
she conclude that none of the women have a blood pressure greater than 110? Why?
18. In a certain town, 60% of adults have a college
degree. The accompanying table describes the
probability distribution for the number of adults
(among 4 randomly selected adults) who have a
college degree. Find the standard deviation for
the probability distribution. Round to the nearest
hundredth.
x
0
1
2
3
4
P(x)
0.0256
0.1536
0.3456
0.3456
0.1296
19. A car insurance company has determined that 6% of all drivers were involved in a car accident last year. Among
the 13 drivers living on one particular street, 3 were involved in a car accident last year. If 13 drivers are
randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year?
Round to three decimal places.
20. Using the following uniform density curve, answer the question.
What is the probability that the random variable has a value greater than 5? Round to three decimal places.
21. Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial
probability formula to find the probability of x successes given the probability p of success on a single trial.
n=6, x=3, p=0.45
STA 2023 – Test #3 Practice
Name _______________________
22. A candy company claims that 24% of its plain candies are orange, and a sample of 200 such candies is randomly
selected.
a. Find the mean and standard deviation for the number of orange candies in such groups of 200.
b. A random sample of 200 candies contains 50 orange candies. Is this result unusual? Does it seem that
the claimed rate of 24% is wrong?
23. Assume the readings on thermometers are normally distributed with a mean of 0C and a standard deviation of
1.00C. Find the probability that a randomly selected thermometer reads greater than -2.24C and draw a
sketch of the region.
24. Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally
distributed with a mean of 100 and a standard deviation of 15.
25. The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 106 inches,
and a standard deviation of 12 inches. What is the probability that the mean annual snowfall during 36
randomly picked years will exceed 108.8 inches? Round your answer to four decimal places.