Download 1. Which of the following is an example of a discrete random variable?

1. Which of the following is an example of a discrete random variable?
A) The length of a window frame
B) The number of horses owned by a farmer
C) The weight of a box of cookies
D) The distance from home to work for a worker
Use the following to answer questions 2-5:
The following table lists the probability distribution of a discrete random variable x:
x
P(x)
2
0.15
3
0.3
4
0.21
5
0.13
6
0.13
7
0.06
8
0.02
2. The probability of x = 7 is:
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3. The probability that x is greater than 6 is:
4. The probability that x is less than or equal to 4 is:
5. The probability that x assumes a value from 3 to 6 is:
6. A survey show that out of 1,000 households surveyed, 459 own one car, 360 own two cars, 156 own three cars,
and 25 own 4 or more cars. Construct the probability distribution for this data.
Use the following to answer question 7:
The following table lists the probability distribution of a discrete random variable x:
x
P(x)
2
0.15
3
0.3
4
0.21
5
0.13
6
0.13
7
0.06
8
0.02
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7. The mean of the random variable x is:
8. 67% of children in a school do not have cavities. Let x be the number of children in a random sample of 50
children selected from this school who do not have cavities. The mean and standard deviation of the probability
distribution of x, rounded to two decimal places, are:
Use the following to answer question 9:
The following table lists the probability distribution of a discrete random variable x:
x
P(x)
2
0.15
3
0.3
4
0.21
5
0.13
6
0.13
7
0.06
8
0.02
9. The standard deviation of the random variable x, rounded to three decimal places, is:
10. Which of the following is not a binomial experiment?
A) Rolling a die 25 times and observing for an even or odd number
B) Randomly selecting 50 items from a production line and observing if they are good or defective
C) Rolling a die 20 times and observing for a number that is less than or equal to 4 or greater than 4
D) Selecting 50 adults and observing if they are in favor of an issue, against it, or have no opinion
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11. Thirty-two percent of adults did not visit their physicians' offices last year. The probability, rounded to four
decimal places, that in a random sample of 7 adults, exactly 2 will say they did not visit their physicians' offices
last year is:
12. Thirty percent of law students who sit for a bar exam pass it the first time. The probability, rounded to four
decimal places, that in a random sample of 15 law students who will sit for the bar examination, at most 2 will
pass it the first time is:
Use the following to answer questions 13-14:
Historical data indicates that Rickenbacker Airlines receives an average of 2.9 complaints per day.
13. What is the probability, rounded to four decimal places, that on a given day, Rickenbacker Airlines will receive
exactly 1 complaints?
14. What is the probability, rounded to four decimal places, that on a given day, Rickenbacker Airlines will receive
less than 5 complaints?
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15. For the standard normal distribution, the area between z = 0 and z = –1.65, rounded to four decimal places, is:
16. For the standard normal distribution, the area to the left of z = –0.47, rounded to four decimal places, is:
17. For the standard normal distribution, the area between z = –1.41 and z = 2.10, rounded to four decimal places, is:
18. There are 250 players in a particular youth soccer league that has 11 teams. The league statistician is tabulating
the total goals scored over the past season by each player. She assigns the random variable y to represent these
totals, and then assigns the following categories for y: 0 to less than 4, 4 to less than 8, 8 to less than 12, 12 to
less than 16, 16 to less than 20, and 20 to less than 24. The relative frequency density for the 8 to less than 12
class is 0.057. How many of the players scored between 8 and less than 12 goals?
19. According to the Empirical rule, 95.44% of the data would fall between what two values for a population with
mean of 408 and standard deviation of 78?
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20. Let x have a normal distribution with a mean of 106.9 and a standard deviation of 12.17. The z value for x =
95.31, rounded to two decimal places, is:
Use the following to answer question 21:
The GMAT scores of all examinees who took that test this year produce a distribution that is approximately normal with
a mean of 450 and a standard deviation of 32.
21. The probability that the score of a randomly selected examinee is more than 530, rounded to four decimal
places, is:
Use the following to answer questions 22-24:
The net weights of all boxes of Top Taste cookies produce a distribution that is approximately normal with a mean of
32.93 and a standard deviation of 0.54.
22. The probability that the net weight of a randomly selected box of these cookies is more than 32.6 ounces,
rounded to four decimal places, is:
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23. The probability that the net weight of a randomly selected box of these cookies is less than 31.58 ounces,
rounded to four decimal places, is:
24. The probability that the net weight of a randomly selected box of these cookies is between 31.8 and 32.5 ounces,
rounded to four decimal places, is:
25. The area under the standard normal curve from zero to z is 0.3849 and z is negative. The value of z is:
26. The area under the standard normal curve to the left of z is 0.0096 and z is negative. The value of z is:
27. Let x be a continuous random variable that follows a normal distribution with a mean of 205 and a standard
deviation of 36.
Find the value of x so that the area under the normal curve to the right of x is approximately 0.0068. Round your
answer to two decimal places.
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28. Let x be a continuous random variable that follows a normal distribution with a mean of 206 and a standard
deviation of 44.
Find the value of x so that the area under the normal curve between µ and x is approximately 0.4920 and the
value of x is greater than µ . Round your answer to two decimal places.
Use the following to answer questions 29-30:
In a recent Gallup poll, 56% of parents with children under 18 years of age gave themselves a grade of B for the job they
are doing bringing up their kids. Assume that this percentage is true for the current population of all parents with children
under 18 years of age. You take a random sample of 991 such parents and ask them to give themselves a grade for the job
they are doing bringing up their kids.
29. The probability that 550 or less will give themselves a grade of B is approximately: (Round the answer to 4
decimal places.)
30. The probability that 520 to 555 will give themselves a grade of B is approximately: (Round the answer to 4
decimal places.)
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Answer Key
1.
2.
3.
4.
5.
6.
7.
8A.
8B.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
B
0.06
0.08
0.66
0.77
Number of cars
owned
1
2
3
4 or more
Probability
0.459
0.36
0.156
0.025
4.05
The mean is 33.50.
The standard deviation is 3.32.
1.552
D
0.3127
0.1268
0.1596
0.8318
0.4505
0.3192
0.9029
57
252 and 564
–0.95
0.0062
0.7294
0.0062
0.1947
–1.20
–2.34
293.92
312.04
0.3877
0.5022
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