Practice Test 2
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. A probability distribution showing the probability of x successes in n trials, where the probability of success
does not change from trial to trial, is termed a
a. uniform probability distribution
b. binomial probability distribution
c. hypergeometric probability distribution
d. normal probability distribution
2. A continuous random variable may assume
a. any value in an interval or collection of intervals
b. only integer values in an interval or collection of intervals
c. only fractional values in an interval or collection of intervals
d. only the positive integer values in an interval
Exhibit 5-1
The following represents the probability distribution for the daily demand of microcomputers at a local store.
Demand
0
1
2
3
4
____
____
____
Probability
0.1
0.2
0.3
0.2
0.2
3. Refer to Exhibit 5-1. The expected daily demand is
a. 1.0
b. 2.2
c. 2, since it has the highest probability
d. of course 4, since it is the largest demand level
4. In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100
feet of material. The probability distribution that has the greatest chance of applying to this situation is the
a. normal distribution
b. binomial distribution
c. Poisson distribution
d. uniform distribution
5. Which of the following is not a characteristic of an experiment where the binomial probability distribution is
applicable?
a. the experiment has a sequence of n identical trials
b. exactly two outcomes are possible on each trial
c. the trials are dependent
d. the probabilities of the outcomes do not change from one trial to another
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____
____
____
____
____
____
____
____
6. The hypergeometric probability distribution is identical to
a. the Poisson probability distribution
b. the binomial probability distribution
c. the normal distribution
d. None of these alternatives is correct.
7. In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven
trials?
a. 0.0036
b. 0.06
c. 0.0554
d. 0.28
8. For a uniform probability density function,
a. the height of the function can not be larger than one
b. the height of the function is the same for each value of x
c. the height of the function is different for various values of x
d. the height of the function decreases as x increases
9. The probability density function for a uniform distribution ranging between 2 and 6 is
a. 4
b. undefined
c. any positive value
d. 0.25
10. A continuous probability distribution that is useful in describing the time, or space, between occurrences of an
event is a(n)
a. normal probability distribution
b. uniform probability distribution
c. exponential probability distribution
d. Poisson probability distribution
11. Larger values of the standard deviation result in a normal curve that is
a. shifted to the right
b. shifted to the left
c. narrower and more peaked
d. wider and flatter
12. Given that Z is a standard normal random variable, what is the probability that -2.51  Z  -1.53?
a. 0.4950
b. 0.4370
c. 0.0570
d. 0.9310
13. Given that Z is a standard normal random variable, what is the probability that -2.08  Z  1.46?
a. 0.9091
b. 0.4812
c. 0.4279
d. 0.0533
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Exhibit 6-3
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
____ 14. Refer to Exhibit 6-3. The probability density function has what value in the interval between 20 and 28?
a. 0
b. 0.050
c. 0.125
d. 1.000
____ 15. Refer to Exhibit 6-3. The probability that X will take on a value of at least 26 is
a. 0.000
b. 0.125
c. 0.250
d. 1.000
Exhibit 6-4
f(x) =(1/10) e-x/10
x0
____ 16. Refer to Exhibit 6-4. The probability that x is less than 5 is
a. 0.6065
b. 0.0606
c. 0.3935
d. 0.9393
Exhibit 6-7
The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard
deviation of 2 ounces.
____ 17. Refer to Exhibit 6-7. What percentage of items will weigh at least 11.7 ounces?
a. 46.78%
b. 96.78%
c. 3.22%
d. 53.22%
Exhibit 6-8
The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard
deviation of 5,000 miles.
____ 18. Refer to Exhibit 6-8. What is the probability that a randomly selected tire will have a life of at least 30,000
miles?
a. 0.4772
b. 0.9772
c. 0.0228
d. 0.5000
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____ 19. The ages of students at a university are normally distributed with a mean of 21. What percentage of the
student body is at least 21 years old?
a. It could be any value, depending on the magnitude of the standard deviation
b. 50%
c. 21%
d. 1.96%
____ 20. Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.9382?
a. 1.8
b. 1.54
c. 2.1
d. 1.77
____ 21. Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is
0.9834?
a. 0.4834
b. -2.13
c. +2.13
d. zero
____ 22. A simple random sample of 100 observations was taken from a large population. The sample mean and the
standard deviation were determined to be 80 and 12 respectively. The standard error of the mean is
a. 1.20
b. 0.12
c. 8.00
d. 0.80
____ 23. In point estimation
a. data from the population is used to estimate the population parameter
b. data from the sample is used to estimate the population parameter
c. data from the sample is used to estimate the sample statistic
d. the mean of the population equals the mean of the sample
____ 24. If we consider the simple random sampling process as an experiment, the sample mean is
a. always zero
b. always smaller than the population mean
c. a random variable
d. exactly equal to the population mean
____ 25. A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50.
Fifty is a
a. population parameter
b. biased estimate of the population mean
c. sample parameter
d. point estimate
____ 26. There are 6 children in a family. The number of children defines a population. The number of simple random
samples of size 2 (without replacement) that are possible equals
a. 12
b. 15
c. 3
d. 16
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____ 27. A sample of 92 observations is taken from an infinite population. The sampling distribution of is
approximately
a. normal because is always approximately normally distributed
b. normal because the sample size is small in comparison to the population size
c. normal because of the central limit theorem
d. None of these alternatives is correct.
____ 28. A sample of 66 observations will be taken from an infinite population. The population proportion equals 0.12.
The probability that the sample proportion will be less than 0.1768 is
a. 0.0568
b. 0.0778
c. 0.4222
d. 0.9222
____ 29. Given two unbiased point estimators of the same population parameter, the point estimator with the smaller
variance is said to have
a. smaller relative efficiency
b. greater relative efficiency
c. smaller consistency
d. larger consistency
____ 30. The number of different simple random samples of size 5 that can be selected from a population of size 8 is
a. 40
b. 336
c. 13
d. 56
____ 31. The following data was collected from a simple random sample of a population
13
15
14
16
12
The point estimate of the population mean
a. cannot be determined, since the population size is unknown
b. is 14
c. is 4
d. is 5
____ 32. The following data was collected from a simple random sample of a population.
13
15
14
16
12
The point estimate of the population standard deviation is
a. 2.500
b. 1.581
c. 2.000
d. 1.414
____ 33. Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and
100 said "no." The point estimate of the proportion in the population who will respond "no" is
a. 75
b. 0.25
c. 0.75
d. 0.50
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____ 34. If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is
a. 0.485
b. 1.96
c. 0.95
d. 1.645
____ 35. In order to use the normal distribution for interval estimation of  when  is known, the population
a. must be very large
b. must have a normal distribution
c. can have any distribution
d. must have a mean of at least 1
____ 36. From a population that is not normally distributed and whose standard deviation is not known, a sample of 20
items is selected to develop an interval estimate for .
a. The normal distribution can be used.
b. The t distribution with 19 degrees of freedom must be used.
c. The t distribution with 20 degrees of freedom must be used.
d. The sample size must be increased.
____ 37. In general, higher confidence levels provide
a. wider confidence intervals
b. narrower confidence intervals
c. a smaller standard error
d. unbiased estimates
____ 38. When the level of confidence increases, the confidence interval
a. stays the same
b. becomes wider
c. becomes narrower
d. becomes narrower for small sample sizes
____ 39. The following random sample was collected.
10
12
18
16
The 80% confidence interval for  is
a. 12.054 to 15.946
b. 10.108 to 17.892
c. 10.321 to 17.679
d. 11.009 to 16.991
____ 40. Which of the following best describes the form of the sampling distribution of the sample proportion?
a. When standardized, it is exactly the standard normal distribution.
b. When standardized, it is the t distribution.
c. It is approximately normal as long as n  30.
d. It is approximately normal as long as np  5 and n(1-p)  5.
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Question 1:
a. Thirty-two percent of the students in a management class are graduate students. A random sample of 5 students is
selected. Using the binomial probability function, determine the probability that the sample contains exactly 2 graduate
students?
b. Using the same values as in (a) find the probability that 1 or less students in the sample are graduate students.
c. Find the mean, variance, and standard deviation.
Question 2:
a. When a particular machine is functioning properly, 80% of the items produced are non-defective. If three items are
examined, what is the probability that one is defective? Use the binomial probability function to answer this question.
b. Find the mean, variance, and standard deviation.
c. What is the probability that if you examine 3 items P(X ≥ 2)? Ie at least 2 are defective.
Questions 3:
A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is
known that the standard deviation of the population is $40.00.
a.
Determine the standard error of the mean.
b.
With a 0.95 probability, determine the margin of error.
c.
What is the 95% confidence interval of the population mean?
Questions 4:
In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 36 pieces of carry-on
luggage was weighed. The average weight was 20 pounds. Assume that we know the standard deviation of the
population to be 8 pounds.
a.
Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage.
b.
Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.
If you are given that the proportion of students at OCCC who have taken calculus is 30%. Use a sample size of n=40.
c. Find the standard deviation of the proportion
d. Use your value in part c to find a 95% CI for students who have taken calculus as OCCC.
Question 5:
The price of a particular brand of jeans has a mean of $37.99 and a standard deviation of $7. A sample of 49 pairs of
jeans is selected. Use Excel to answer the following questions.
a. What is the probability that the sample of jeans will have a mean price less than $40?
b. What is the probability that the sample of jeans will have a mean price between $38 and $39?
c. What is the probability that the sample of jeans will have a mean price within $3 of the population mean?
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Question 6
The sales records of a real estate agency show the following sales over the past 200 days:
Number of Houses Sold # Days
a.
b.
c.
d.
e.
f.
g.
0
60
1
80
2
40
3
16
4
4
How many sample points are there?
Assign probabilities to the sample points and show their values.
What is the probability that the agency will not sell any houses in a given day?
What is the probability of selling at least 2 houses?
What is the probability of selling 1 or 2 houses?
What is the probability of selling less than 3 houses?
Find the mean, variance, and standard deviation of the distribution.
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