1. If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A∩B) is
A 0
B 0.24
C 1
D 0.8
E 1.5
2. The number of telephone calls received in a sample of five consecutive hours is
3 5 12 3 2
The coefficient of variation is
A 72.7%
B 81.2%
C 123%
D 363%
E none of the above
Use the following information to answer questions 3. and 4.
A diligent collector of waste aluminium cans collects the following number of cans on fifteen consecutive days.
40 25 35 30 25 20 30 40 20 30 10 30 20 10 5
3. The median number of cans is
A 40
B 30
C 25
D 20
E none of the above
4. The 40th percentile is
A 20
B 25
C 6
D 22.5
E none of the above
Use the following information to answer questions 5. and 6.
A bottling company uses a filling machine to fill plastic bottles with a popular brand of cola. The bottles are supposed to contain 300 ml. In fact, the contents vary according to a normal distribution with mean μ = 298 and standard deviation σ = 3ml.
5. What is the probability that a randomly selected bottle contains less than 295 ml?
A 0.3413
B 0.8413
C 0.4525
D 0.0475
E 0.1587
6. What is the probability that the average volume of the contents of the bottles of a six-pack is less than 296 ml?
A 0.2486
B 0.2514
C 0.4484
D 0.0516
E none of the above
7. A six sided die is tossed 5 times. The probability of observing five ones is
A 1/6
B 5/6
C 1
D 1/7776
E none of the above
8. The reason why the standard deviation of a distribution is more easily interpreted than the variance is that
A it is a measure of average deviation.
B it is expressed in the same units as the data.
C it takes every data value into account.
D it is standardised.
E it takes the mean into account.
9. One regular feature of the local news is the weather forecast, where the probability of rain is usually given. If this probability is determined by calculating the percentage of past days with similar weather conditions on which rain occurred, which method of probability has been used to determine the probability of rain?
A The classical method.
B The subjective method.
C Either the subjective method or the classical method.
D The relative frequency method.
E The posterior probability method.
Use the following information to answer questions 10. 11. and 12.
The 600 employees of a company were surveyed as to their educational background and marital status. The results of the survey are provided in the table below.
Single Married Totals
Has a University Degree 40 310 350
Does not have a University Degree 60 190 250
Totals 100 500 600
10. What is the probability that an employee is single?
A 0.167
B 0.400
C 0.600
D 0.067
E 0.100
11. What is the probability that an employee of the company is single or has a University degree?
A 0.067
B 0.333
C 0.750
D 0.683
E none of the above
12. If the employee is single, what is the probability that he/she does not have a University degree?
A 0.167
B 0.400
C 0.600
D 0.067
E 0.100
13. Maria Leeson, who operates a telephone message service, gets calls at an average rate of 2 calls per minute. What is the probability that Maria will receive exactly 5 calls in a given minute.
A 0.135
B 0.036
C 0.002
D 0.947
E 0.983
14. Which of the following statements about the approximation for binomial probabilities is correct?
A If p = 0.01 and n = 100, either the Poisson or the normal approximation would provide good approximate probabilities.
B If p = 0.97 and n = 50, the Poisson approximation would provide good approximate probabilities.
C If p = 0.1 and n = 100, the normal approximation would provide good approximate probabilities.
D In any case where the Poisson approximation is applicable, the normal approximation could also be used.
E None of the above.
15. Howard is a high school basketball player. The team's coach watched Howard take 60 free throws over several training sessions. Howard made 39 of these. What is the best point estimate for the standard error of the proportion?
A 0.0616
B 0.0700
C 0.0764
D 0.1041
E none of the above
16. Eileen, a waitress, wants to gain some idea about the amount of money she can make in tips per day. She randomly chooses seven days in a typical month and finds the mean to be x‾ = $21 and the standard deviation to be s = $3.70. A 90% confidence interval for Eileen's average daily tips would be
A 21 ± 2.013
B 21 ± 2.717
C 21 ± 2.650
D 21 ± 2.300
E none of the above
17. If a researcher wants to obtain the mean income of a certain area correct to within $100 with a probability of 0.95, what size random sample should he take if he knows that the standard deviation of the incomes is $600?
A 553.2
B 554
C 138.3
D 139
E 196
18. Y is a normally distributed random variable with mean and standard deviation σ = 2. If P(Y < c) the value of c is
A 11.68
B 8.96
C 8.32
D 11.04
E -8.32
19. Based on historical records, a rental establishment has determined that the probability distribution of the number of daily rentals (X) of a piece of equipment is as follows:
x 0 1 2 3 4
P(x) 0.10 0.25 0.40 0.20 0.05
If the establishment charges $25 per rental, the expected daily income from the rentals of this equipment are
A $1.85
B $26.85
C $46.25
D $25.00
E none of the above
20. The probability that a certain electrical component will work is 0.9. A machine contains five such components. The machine will operate as long as at least three of these components works. What is the probability that the machine will operate?
A 0.009
B 0.081
C 0.072
D 0.410
E 0.991