Use the following information to answer question 1. and 2.
A manufacturer of torch batteries took a sample of 13 batteries from one day's production and used them continuously until they were drained. The number of hours they were used until failure were
342 426 317 545 264 451 1049
631 512 266 492 562 298
1. Which of the following statements about the descriptive statistics for these data are correct?
A. the mean = 473.5 and the median = 451
B. the mean = 473.4 and there is no mode;
C. the range = 785 and the median = 426
D. the range = 785 and the mean = 473.4
E. the median = 426 and the mean = 473.4
2. The coefficient of variation is
A. 1.66
B. 0.45
C. 0.43
D. 210.77
E. 202.50
3. The amount of heat is measured by temperature. Which type of scale is a measurement of temperature?
A. a nominal scale
B. a discrete scale
C. a ratio scale
D. an ordinal scale
E. an interval scale.
4. Which of the measures of dispersion is least affected by the presence of extreme values
A. standard deviation
B. range
C. interquartile range
D. variance
E. median
5. The following boxplot was constructed in Excel. Which of the following statements about the data set described by this boxplot is most correct?
A. The mean is approximately 10.5.
B. The data appear to be negatively skewed.
C. The data appear to be positively skewed.
D. Both A. and B. are correct.
E. Both A. and C. are correct.
6. One of the differences between a binomial distribution and a Poisson distribution is that
A. in the binomial distribution, there is no specified number of possible trials.
B. in the binomial distribution, the distribution depends only on the mean number of occurrences expected.
C. in the Poisson distribution, there is no specified number of trials.
D. in the Poisson distribution, each time the random experiment is run, either the event happens or it doesn't.
E. in the Poisson distribution, each time the random experiment is run, the probability of a success remains constant.
7. If P(A) = 0.2, P(B) = 0.4 the joint probability of A and B is 0.08, then events A and B are
A. mutually exclusive.
B. dependent.
C. conditional.
D. equal.
E. independent.
Use the information following to answer questions 8. and 9.
You are planning to make sales calls to eight firms today. As a rough approximation, you estimate that each call has a 20% chance of resulting in a sale and that firms make their buying decision without consulting each other.
8. Find the probability of making exactly three sales today.
A. 0.797
B. 0.147
C. 0.944
D. 0.008
E. 0.003
9. Find the probability of making more than one sale today.
A. 0.797
B. 0.203
C. 0.503
D. 0.497
E. 0.832
10. Which of the following samples is likely to be the most representative of the population of all employees at IBM?
A. The ten oldest and most experienced researchers in the research department of IBM.
B. A random sample of 10 computer repair specialists.
C. Five male and five female IBM employees.
D. The ten employees selected as ‘typical' by middle management.
E. A random sample of ten, chosen from a list of all employees at IBM.
11. If Z is the standard normal random variable, then P(Z < 1.7) is
A. 0.9554
B. 0.4554
C. 0.0446
D. 0.9545
E. 0.8577
12. If Z is the standard normal random variable, then P(-2.3 ≤ Z ≤ -0.2) is
A. 0.4100
B. 0.5686
C. 0.5900
D. 0.4813
E. 0.5793
Use the following information to answer questions 13., 14. and 15.
Wages for workers in a particular industry are normally distributed with a mean of $11.90 per hour and a standard deviation of $0.40.
13. What percentage of workers receive wages less than $11.00?
A. 48.78%
B. 98.78%
C. 48.75%
D. 1.25%
E. 1.22%
14. What must the wage be if only 10% of all workers in this industry earn more?
A. $11.94
B. $11.86
C. $12.41
D. $12.42
E. $11.39
15. What is the probability a random sample of 20 workers has an average wage of more than $12.00?
A. 0.0987
B. 0.4013
C. 0.3686
D. 0.1314
E. 0.6314
16. The number of orders for the installation of computer information systems received by an agency each week is a random variable, x, with the following probability distribution.
x p(x)
0 0.10
1 0.20
2 0.30
3 0.15
4 0.15
5 0.05
6 0.05
The mean and standard deviation of the number of orders for installation are
A. 2.4 and 2.44 respectively.
B. 2.4 and 1.56 respectively
C. 2.4 and 3 respectively
D. 3 and 2.44 respectively
E. 3 and 1.56 respectively
Use the following information to answer questions 17. and 18.
A natural gas exploration company averages four strikes per 100 holes drilled, and strikes occur randomly and independently.
17. If 100 holes are to be drilled, what is the probability exactly five strikes will be made?
A. 0.785
B. 0.156
C. 0.000
D. 0.04
E. 0.200
18. If 25 holes are to be drilled, what is the probability that at least two strikes will be made?
A. 0.736
B. 0.920
C. 0.238
D. 0.908
E. 0.264
19. The probability that a certain component will work is 0.9. A machine contains 3 such components. The machine will operate as long as at least two of these components are working. What is the probability that the machine will operate?
A. 0.972
B. 0.081
C. 0.243
D. 0.729
E. 0.810
20. The following data represent the fuel consumption of 100 identical new small cars.
Fuel consumption (km per litre) Number of cars
> 9 up to and including 10 5
> 10 up to and including 11 7
> 11 up to and including 12 10
> 12 up to and including 13 15
> 13 up to and including 14 20
> 14 up to and including 15 25
> 15 up to and including 16 15
> 16 up to and including 17 3
The approximate mean and standard deviation fuel consumption for this sample are
A. 13.38 and 1.765 km/litre respectively.
B. 13.38 and 1.757 km/litre respectively.
C. 13.43 and 1.765 km/litre respectively
D. 13.43 and 1.757 km/litre respectively.
E. 13 and 1.765 km/litre respectively.