Stat Homework
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Stat1046.1HW3.docxStat 104 Chapter 6 Name:________________________
6.1 Homework
page 322-324 #5, 9, 17, 23, 25, 27. 29, 30, 31, 39, 45, 49, 53, 57, 63
5. What are the two rules for a discrete probability distribution?
9. Indicate whether the variable is a discrete or continuous random variable: How much coffee will be in your next cup of coffee.
17. Shirelle enjoys listening to album downloads while doing her homework. The probabilities that she will listen to X = 0, 1, 2, 3, or 4 album downloads tonight are 6%, 24%, 38%, 22%, and 10%, respectively.
a. Construct a probability distribution table.
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b. Construct a probability distribution graph.
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23. For 2014, the College Board reported that 742,000 students had 4 years of high school math, 209,000 had three years of high school math, 30,000 had two years, and 13,000 had one year of high school math when they took their SAT exams.
a. Construct a probability distribution table.
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b. Construct a probability distribution graph.
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Determine whether the following distributions represent a valid probability distribution. If it does not, explain why not.
25.
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X |
-10 |
0 |
10 |
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P(X) |
1/5 |
1/2 |
1/5 |
27.
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X |
1 |
2 |
3 |
4 |
5 |
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P(X) |
-0.5 |
0.5 |
0.7 |
0.1 |
0.2 |
The National Hockey League Championship is decided by a best-of-seven playoff called the Stanley Cup Finals. The following table shows the possible values of X= number of games in the series and the frequency of each value of X, for the Stanley Cup Finals between 1990 and 2014.
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X = games |
Frequency |
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4 |
5 |
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5 |
5 |
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6 |
7 |
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7 |
7 |
Find the probability that a randomly chosen NHL Championship will have the following number of games:
29. At least six games, X ≥ 6
30. At most six games, X ≤ 6
31. Between 5 and 7 games, inclusive, 5 ≤ X ≤ 7
39. Refer to the probability distribution you calculated in problem #23. Find the probability that a randomly chosen student will have taken either 3 or 4 years of math, i.e. X = 3 or X = 4.
45. For X = the number of album downloads from problem #17:
a. Calculate the mean value of X, µ.
b. Identify the most likely value of X.
c. Find the expected value of X, E(X).
49. For X = the number of games from problems #21, 29-31:
a. Calculate the mean value of X, µ.
b. Identify the most likely value of X.
c. Find the expected value of X, E(X).
53. For X = the number of album downloads from problem #17:
a. Compute the variance of X, ơ2.
b. Calculate the standard deviation of X, ơ.
c. Use the Z score method to determine whether any outliers or unusual data values exist.
57. For X = the number of games from problems #21, 29-31, 49:
a. Compute the variance of X, ơ2.
b. Calculate the standard deviation of X, ơ.
c. Use the Z score method to determine whether any outliers or unusual data values exist.
63. The New York City Police Department tracks the number of vehicles involved in each vehicle collision that occurs in Manhattan. The table shows the frequency distribution for X = the number of vehicles involved in collisions in Manhattan in July 2014.
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X = vehicles involved |
Frequency |
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1 |
288 |
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2 |
3151 |
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3 |
109 |
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4 |
12 |
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5 |
4 |
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8 |
1 |
a. Construct a probability distribution table for X.
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b. Find the probability that at least three vehicles are involved in a collision.
c. Find the probability that 6 vehicles are involved in a collision.
d. Find P(1 ≤ X ≤ 3)
e. Calculate P(1 < X < 3).
Stat 104 6.1 HW
Fall 2020 Instructor J Hodgson Page 1 of 2
