Download ACTV-LRNG-6

Active Learning Lecture Slides
For use with Classroom Response Systems
Probability Distributions
6.1 All students in a class were asked how many times
they had read the city newspaper in the past 5 days.
The data is in the chart below. What proportion read the
newspaper more than 3 times in the past 5 days?
a)
b)
c)
d)
e)
0.1
0.5
0.6
1.0
None of the above
Copyright © 2013 Pearson Education, Inc.
No. Times
Read
Newspaper
Probability
0
0.25
1
0.05
2
0.10
3
0.10
4
0.15
5
0.35
6.1 All students in a class were asked how many times
they had read the city newspaper in the past 5 days.
The data is in the chart below. What proportion read the
newspaper more than 3 times in the past 5 days?
a)
b)
c)
d)
e)
0.1
0.5
0.6
1.0
None of the above
Copyright © 2013 Pearson Education, Inc.
No. Times
Read
Newspaper
Probability
0
0.25
1
0.05
2
0.10
3
0.10
4
0.15
5
0.35
6.2 All students in a class were asked how many times
they had read the city newspaper in the past 5 days.
The data is in the chart below. What is the expected
number of times that someone will have read the
newspaper in the past 5 days?
a)
b)
c)
d)
e)
2.5
2.9
3
3.9
None of the above
Copyright © 2013 Pearson Education, Inc.
No. Times
Read
Newspaper
Probability
0
0.25
1
0.05
2
0.10
3
0.10
4
0.15
5
0.35
6.2 All students in a class were asked how many times
they had read the city newspaper in the past 5 days.
The data is in the chart below. What is the expected
number of times that someone will have read the
newspaper in the past 5 days?
a)
b)
c)
d)
e)
2.5
2.9
3
3.9
None of the above
Copyright © 2013 Pearson Education, Inc.
No. Times
Read
Newspaper
Probability
0
0.25
1
0.05
2
0.10
3
0.10
4
0.15
5
0.35
6.3 Suppose there is a special new lottery in your
state. Each lottery ticket is worth $20 and gives you a
chance at being selected to win $2,000,000. There is
a 0.0001% chance that you will be selected and win
otherwise, you win nothing. Let X denote your
winnings. What is the expected value of X?
a) $2
b) $0
c) $2,000,000
d) $1,999,980
e) $200
Copyright © 2013 Pearson Education, Inc.
6.3 Suppose there is a special new lottery in your
state. Each lottery ticket is worth $20 and gives you a
chance at being selected to win $2,000,000. There is
a 0.0001% chance that you will be selected and win
otherwise, you win nothing. Let X denote your
winnings. What is the expected value of X?
a) $2
b) $0
c) $2,000,000
d) $1,999,980
e) $200
Copyright © 2013 Pearson Education, Inc.
6.4 Suppose that a random number generator can
generate any number, including decimals, between
0 and 10 with any value being equally likely to be
chosen. What is the probability that a number is
drawn between 7 and 10?
a) 0.4
b) 0.3
c) 0.2
d) 0.1
e) 0.273
Copyright © 2013 Pearson Education, Inc.
6.4 Suppose that a random number generator can
generate any number, including decimals, between
0 and 10 with any value being equally likely to be
chosen. What is the probability that a number is
drawn between 7 and 10?
a) 0.4
b) 0.3
c) 0.2
d) 0.1
e) 0.273
Copyright © 2013 Pearson Education, Inc.
6.5 Suppose that a random number generator can
generate any number, including decimals, between
0 and 10 with any value being equally likely to be
chosen. What would be the mean of this
distribution?
a) 4.5
b) 5
c) 5.5
d) 6
e) Cannot be determined
Copyright © 2013 Pearson Education, Inc.
6.5 Suppose that a random number generator can
generate any number, including decimals, between
0 and 10 with any value being equally likely to be
chosen. What would be the mean of this
distribution?
a) 4.5
b) 5
c) 5.5
d) 6
e) Cannot be determined
Copyright © 2013 Pearson Education, Inc.
6.6 Which of the following is NOT a property of
the normal distribution?
a) It is symmetric.
b) It is bell-shaped.
c) It is centered at the mean, 0.
d) It has a standard deviation,  .
e) All of the above are correct.
Copyright © 2013 Pearson Education, Inc.
6.6 Which of the following is NOT a property of
the normal distribution?
a) It is symmetric.
b) It is bell-shaped.
c) It is centered at the mean, 0.
d) It has a standard deviation,  .
e) All of the above are correct.
Copyright © 2013 Pearson Education, Inc.
6.7 Scores on the verbal section of the SAT have
a mean of 500 and a standard deviation of 100.
Scores are approximately normally distributed.
What proportion of SAT scores are higher than
450?
a) 0.5
b) 0.5557
c) 0.6915
d) 0.3085
e) 0.7257
Copyright © 2013 Pearson Education, Inc.
6.7 Scores on the verbal section of the SAT have
a mean of 500 and a standard deviation of 100.
Scores are approximately normally distributed.
What proportion of SAT scores are higher than
450?
a) 0.5
b) 0.5557
c) 0.6915
d) 0.3085
e) 0.7257
Copyright © 2013 Pearson Education, Inc.
6.8 Scores on the verbal section of the SAT have
a mean of 500 and a standard deviation of 100.
Scores are approximately normally distributed. If
someone scored at the 90th percentile, what is
their SAT score?
a) 608
b) 618
c) 628
d) 638
e) 648
Copyright © 2013 Pearson Education, Inc.
6.8 Scores on the verbal section of the SAT have
a mean of 500 and a standard deviation of 100.
Scores are approximately normally distributed. If
someone scored at the 90th percentile, what is
their SAT score?
a) 608
b) 618
c) 628
d) 638
e) 648
Copyright © 2013 Pearson Education, Inc.
6.9 What is the standard normal distribution?
a)
b)
c)
d)
e)
N ( , )
N ( ,  )
N (1,0)
N (0,1)
N ( z, z )
Copyright © 2013 Pearson Education, Inc.
6.9 What is the standard normal distribution?
a)
b)
c)
d)
e)
N ( , )
N ( ,  )
N (1,0)
N (0,1)
N ( z, z )
Copyright © 2013 Pearson Education, Inc.
6.10 There are two sections of Intro Statistics and they
both gave an exam on the same material. Suppose that
Megan made an 83 in 2nd period and Jose made an 85
in 3rd period. Using the information below. Who scored
relatively higher with respect to their own period?
2nd period
3rd period
Mean
80
82
Standard Deviation
5
6
a) Jose
b) Megan
c) They are the same
d) Cannot be determined
Copyright © 2013 Pearson Education, Inc.
6.10 There are two sections of Intro Statistics and they
both gave an exam on the same material. Suppose that
Megan made an 83 in 2nd period and Jose made an 85
in 3rd period. Using the information below. Who scored
relatively higher with respect to their own period?
2nd period
3rd period
Mean
80
82
Standard Deviation
5
6
a) Jose
b) Megan
c) They are the same
d) Cannot be determined
Copyright © 2013 Pearson Education, Inc.
6.11 Which of the following is NOT a condition of
the binomial distribution?
a) The trials are dependent.
b) There are a set number of trials, n.
c) The probability of success is constant from trial
to trial.
d) There are two possible outcomes.
Copyright © 2013 Pearson Education, Inc.
6.11 Which of the following is NOT a condition of
the binomial distribution?
a) The trials are dependent.
b) There are a set number of trials, n.
c) The probability of success is constant from trial
to trial.
d) There are two possible outcomes.
Copyright © 2013 Pearson Education, Inc.
6.12 Suppose that you flipped an unbalanced coin
10 times. Suppose that the probability of getting
“heads-up” was 0.3 and that X equals the number
of times that you get “heads-up”. If X has a
binomial distribution, what is the probability that
X = 4?
a) 0.20
b) 0.25
c) 0.30
d) 0.50
Copyright © 2013 Pearson Education, Inc.
6.12 Suppose that you flipped an unbalanced coin
10 times. Suppose that the probability of getting
“heads-up” was 0.3 and that X equals the number
of times that you get “heads-up”. If X has a
binomial distribution, what is the probability that
X = 4?
a) 0.20
b) 0.25
c) 0.30
d) 0.50
Copyright © 2013 Pearson Education, Inc.
6.13 Suppose that you flipped an unbalanced coin
10 times. Suppose that the probability of getting
“heads-up” was 0.3 and that X equals the number
of times that you get “heads-up”. If X has a
binomial distribution, what is the expected value
and standard deviation of X?
a) Expected value = 3
b) Expected value = 3
c) Expected value = 0.3
d) Expected value = 0.3
e) Expected value = 3
Copyright © 2013 Pearson Education, Inc.
Standard Deviation = 2.1
Standard Deviation = .145
Standard Deviation = .145
Standard Deviation = 1.45
Standard Deviation = 1.45
6.13 Suppose that you flipped an unbalanced coin
10 times. Suppose that the probability of getting
“heads-up” was 0.3 and that X equals the number
of times that you get “heads-up”. If X has a
binomial distribution, what is the expected value
and standard deviation of X?
a) Expected value = 3
b) Expected value = 3
c) Expected value = 0.3
d) Expected value = 0.3
e) Expected value = 3
Copyright © 2013 Pearson Education, Inc.
Standard Deviation = 2.1
Standard Deviation = .145
Standard Deviation = .145
Standard Deviation = 1.45
Standard Deviation = 1.45
6.14 Suppose that a college level basketball
player has an 80% chance of making a free throw.
Assume that the free throws can be considered
independent of each other. Suppose that he
shoots 8 free throws in a game. What is his
expected number of baskets?
a) 0.8
b) 1
c) 6.4
d) 7.2
Copyright © 2013 Pearson Education, Inc.
6.14 Suppose that a college level basketball
player has an 80% chance of making a free throw.
Assume that the free throws can be considered
independent of each other. Suppose that he
shoots 8 free throws in a game. What is his
expected number of baskets?
a) 0.8
b) 1
c) 6.4
d) 7.2
Copyright © 2013 Pearson Education, Inc.
6.15 Suppose that a college level basketball
player has an 80% chance of making a free throw.
Assume that the free throws can be considered
independent of each other. Suppose that he
shoots 8 free throws in a game. What is the
probability that he makes 7 baskets?
a) 0.042
b) 0.167
c) 0.294
d) 0.336
e) 0.80
Copyright © 2013 Pearson Education, Inc.
6.15 Suppose that a college level basketball
player has an 80% chance of making a free throw.
Assume that the free throws can be considered
independent of each other. Suppose that he
shoots 8 free throws in a game. What is the
probability that he makes 7 baskets?
a) 0.042
b) 0.167
c) 0.294
d) 0.336
e) 0.80
Copyright © 2013 Pearson Education, Inc.