Stat Homework
Smaxwell55
Stat1045.3BHW1.docxStat 104 Chapter 5 Name:________________________
5.3B Homework
page 288 #59, 61, 67, 69, 71, 75, 77, page 289 #79, 85, 93, 100, 101
The National Center for Education Statistics reports the following statistics for surveys of 12,320 female college students and 9,184 male college students:
· 36% of females work 16-25 hours per week
· 38% of males work 16-25 hours per week
A random sample of n=2 college students is taken. Define the following events:
F1: 1st draw is a female who works 16-25 hours per week
F2: 2nd draw is a female who works 16-25 hours per week
M1: 1st draw is a male who works 16-25 hours per week
M2: 2nd draw is a male who works 16-25 hours per week
Use the Multiplication Rule for Independent Events to calculate the indicated probabilities:
59. P(F1 and F2)
61. P(M1 and F2)
Suppose we sample two cards at random and with replacement from a shuffled standard deck of 52 cards. Define the following events:
R1: Red card observed on the first draw.
R2: Red card observed on the second draw.
H1: Heart observed on the first draw.
H2: Heart observed on the second draw.
Find the following probabilities:
67. P(R1 and R2)
69. P(R1 and H2)
Suppose we sample three cards at random and without replacement from a shuffled standard deck of 52 cards. Define the following events:
R1: Red card observed on the first draw.
R2: Red card observed on the second draw.
R3: Red card observed on the third draw.
H1: Heart observed on the first draw.
H2: Heart observed on the second draw.
H3: Heart observed on the third draw.
Find the following probability:
71. P(H1 and R2 and R3)
75. The College Board reports that 48% of the 1.5 million students who took the Natural Sciences subject exam in 2014 had taken 4 years of high school science. If we take a sample of the following number of students, verify that the 1% Guideline applies.
a. n = 2 students
b. n = 3 students
c. n = 5 students
77. Use the 1% Guideline to approximate the probability that n= 3 students who took the Natural Sciences subject exam had taken four years of high school science.
The following contingency table shows the manga (a type of graphic novel) publisher and the weeks on the New York Times Best Seller List for the week of August 24, 2014.
|
|
VIZ Media |
Kodansha |
Seven Seas |
Total |
|
1 week |
3 |
1 |
0 |
4 |
|
2 weeks |
3 |
0 |
1 |
4 |
|
>2 weeks |
0 |
2 |
0 |
2 |
|
Total |
6 |
3 |
1 |
10 |
A manga title is to be selected at random. Define the following events:
V: Manga title is published VIZ Media.
K: Manga title is published by Kodansha.
A: Manga title has been on list for one week.
B: Manga title has been on list for two weeks.
C: Manga title has been on list for more than two weeks.
79. Use the alternative method for determining independence to determine whether the following pair of events are independent: V and A.
85. Determine whether the following mutually exclusive events are independent: V and K.
93. Use the Multiplication Rule for n Independent Events to find the probability that E occurs on three successive tosses if E is defined as Observe an even number on a toss of a fair six sided die.
100. Define H: observe a number greater than 3 on a toss of a fair six sided die.
Find the probability that H occurs at least once in ten tosses.
101. Google reports that 50% of incoming emails to Gmail are encrypted. For the random sample of size 2, find the probability that at least one of the emails is encrypted.
Stat 104 5.3B HW
Fall 2020 Instructor J Hodgson Page 1 of 2
