1. The probability that a continuous random variable takes any specific value
a.
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is equal to zero
b.
is at least 0.5
c.
depends on the probability density function
d.
is very close to 1.0
2. A normal distribution with a mean of 0 and a standard deviation of 1 is called
a.
a probability density function
b.
an ordinary normal curve
c.
a standard normal distribution
d.
none of these alternatives is correct
3. For a continuous random variable X, the probability density function f(x) represents
a.
the probability at a given value of x
b.
the area under the curve at x
c.
the area under the curve to the right of x
d.
the height of the function at x
4. Which of the following is not a characteristic of the normal probability distribution?
a.
the mean, median, and the mode are equal
b.
the mean of the distribution can be negative, zero, or positive
c.
the distribution is symmetrical
d.
the standard deviation must be 1
5. A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is
a.
different for each interval
b.
the same for each interval
c.
at least one
d.
none of these alternatives is correct
6. 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
7. The length of time patients must wait to see a doctor in a local clinic is uniformly distributed between 15 minutes and 2.5 hours. Compute the total number of one-hour intervals in the above interval.
a.
135
b.
2
c.
3
d.
2.25
e.
none of these responses
8. Refer to question 7. Compute the probability that a patient would have to wait between 45 minutes and 2 hours.
a.
135/165
b.
0
c.
75/135
d.
37.5/135
e.
none of these responses
9. Refer to question 7. Compute the probability that the patient would have to wait exactly 50 minutes.
a.
50/135
b.
1/135
c.
0
d.
none of these responses
10. Refer to question 7. Compute the probability that the patient would have to wait over 2 hours.
a.
2/135
b.
30/135
c.
120/135
d.
0
e.
none of these responses
11. Refer to question 7. Compute the expected waiting time and associated standard deviation, respectively.
a.
82.5 minutes; 38.97 minutes
b.
82.5 minutes; 1518.75 minutes
c.
135 minutes; 38.97 minutes
d.
82.5 minutes; 47.63 minutes
e.
135 minutes; 47.63 minutes
12. The time in minutes for which a student uses a computer terminal at the computer center of a major university follows an exponential probability distribution with a mean of 36 minutes. Assume a student arrives at the terminal just as another student is beginning to work on the terminal. What is the probability that the wait for the second student will be 15 minutes or less?
a.
0.659
b.
0.341
c.
0
d.
0.417
13. Refer to question 12. What is the probability that the wait for the second student will be between 15 and 45 minutes?
a.
0.713
b.
0.341
c.
0.833
d.
0.372
14. Refer to question 12. What is the probability that the second student will have to wait an hour or more?
a.
0
b.
0.811
c.
0.600
d.
0.189
15. Assume that the random variable X is defined as the number of minutes it takes to obtain a driver’s license at the local Division of Motor Vehicles (DMV). DMVs are notorious for being slow. Is it plausible, then, that X is distributed exponentially?
a.
yes
b.
no
16. Refer to question 15. Is it plausible that X is distributed uniformly?
a.
yes
b.
no
17. The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. The probability of a player weighing more than 241.25 pounds is
a.
0.4505
b.
0.0495
c.
0.9505
d.
0.9010
18. Refer to question 17. The probability of a player weighing less than 250 pounds is
a.
0.4772
b.
0.9772
c.
0.0528
d.
0.5000
19. Refer to question 17. What percent of players weigh between 180 and 220 pounds?
a.
28.81%
b.
0.5762%
c.
0.281%
d.
57.62%
20. Refer to question 17. What is the minimum weight of the middle 95% of the players?
a.
196 pounds
b.
151 pounds
c.
249 pounds
d.
190 pounds
√
FROM EDONOMICS DAN STUDIES
TABLE 1 STANDARD NORMAL DISTRIBUTION
:. ~.
”
‘-:,
Area or ,··:t
probability
.:.1
.,
Entries in the table give the area under .-,
the curve between the mean and z stan- ···.i
‘. dard deviations above the mean, For
. ,~
..~.’
..
….. \
.. example, for z= ~.25 the area under
..,
the curve between the mean and z is ‘.’
0 z .3944. “,’ . ,.. ~.••. :
Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
.0 .0000 .0040 ,0080 .0120 .0160 .0199 ,0239 .0279 .0319 .0359
.I .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 ,0714 .0753
.2 .0793 .0832 .0871 .0910 ,0948 ,0987 .1026 .1064 .1103 .l141
.,
.3 .1179 .1217 .1255 .1293 .1331 ,1368 .1406 .1443 .1480 .1517
A .1554 .1591 .1628 .1664 .1700 .1736 .1772 ;1808 .1844 .1879. . ,.
.5 .1915 ,1950 .1985 ,2019 .2054 .2088 .2123 .2157 .2190 .2224 ,’;
.6 .2257 ,2291 .2324 .2357 ,2389 .2422 .2454 .2486 .2518 .2549
.7 ,2580 .2794
‘.,
.2612 .2642 ,2673 .2704 .2734 .2764 ,2823 .2852
.8 .288′! .2910 .~106
.~
.2939 ,2967 .2995 .3023 .3051 ,3078 .3133
“t
.9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 3365 3389 .j
1.0 .3413 .3438 .3461 .3485 .3508 .3531 .3554 .3577 .3599 .3621
1.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830
1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015
..
1.3 .4{)32 .4049 .4066 .4{)82 04099 .4115 04131 .4147 .4162 .4171
,
2.0 ,4772 ,4778 .4783 .4788 .4793 .4798 .4803 .4808 .4S12 .4817
2.1 .482l .4826 ,4830 .4834 .4838 .4S42 .4S46 ,4850 .4854 .4857
2.2 ,4861 .4864 ,4868 .4871 .4875 .4878 .4881 .4884 .4887 ,4890
2.3 .4893 .4896 .4898 .4901 .4904 .4906 ,4909 .49 II .4913 .4916
2.4 .4918 .4920 .4922 ,4925 ,4927 .4929 .4931 .4932 .4934 .4936
2.5 .4938 .4940 .4941 .4943 .4945 ,4946 .4948 .4949 ,4951 .495~
2.6 .4953 .4955 .4956 . .4957 .4959 .4960 .4961 .4962 .4963 .4964
2.7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974
2.8 .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 ,4980 .4981
2.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 ,4985 .4986 .4986
3.0 ,4986 .4987 .4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990
··,i.~
12/05/2008 12:39PM (GMT-O~
