Basic Computation: p Distribution Suppose we have a binomial experi- ment in which success is defined to be a particular quality or attribute that interests us. 33 and p = 0.21. Can we approximate the p distribution by (a) Suppose n = a normal distribution? Why? What are the values of µ, and o;? (b) Suppose n = 25 and p = 0.15. Can we safely approximate the p distribu- tion by a normal distribution? Why or why not? (c) Suppose n = 48 and p = 0.15. Can we approximate the p distribution by a normal distribution? Why? What are the values of µ; and o;?
Basic Computation: p Distribution Suppose we have a binomial experi- ment in which success is defined to be a particular quality or attribute that interests us. 33 and p = 0.21. Can we approximate the p distribution by (a) Suppose n = a normal distribution? Why? What are the values of µ, and o;? (b) Suppose n = 25 and p = 0.15. Can we safely approximate the p distribu- tion by a normal distribution? Why or why not? (c) Suppose n = 48 and p = 0.15. Can we approximate the p distribution by a normal distribution? Why? What are the values of µ; and o;?
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 6ECP: In Pennsylvania’s Cash 5 game, a player chooses five different numbers from 1 to 43. If these five...
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
Its number 20.
![S AND SAMPLING DISTRIBUTIONS
15.
Airline Flights: No-Shows Based on long experience, an airline has found
that about 6% of the people making reservations on a flight from Miami to
Denver do not show up for the flight. Suppose the airline overbooks this flight
by selling 267 ticket reservations for an airplane with only 255 seats.
(a) What is the probability that a person holding a reservation will show up
for the flight?
X-
(b) Let n =
267 represent the number of ticket reservations. Let r represent
the number of people with reservations who show up for the flight. Which
expression represents the probability that a seat will be available for
everyone who shows up holding a reservation?
P(255 < r); P(r < 255); P(r < 267); P(r = 255)
(c) Use the normal approximation to the binomial distribution and part (b) to
answer the following question: What is the probability that a seat will be
available for every person who shows up holding a reservation?
16.
General: Approximations We have studied two approximations to the
binomial, the normal approximation and the Poisson approximation
(See Section 5.4). Write a brief but complete essay in which
and summarize the conditions under which each approximation would be
used, the formulas involved, and the assumptions made for each approxima-
tion. Give details and examples in your essay. How could you apply these
statistical methods in your everyday life?
on,
you
discuss
17.
Statistical Literacy Under what conditions is it appropriate to use a normal
distribution to approximate the p distribution?
18.| Statistical Literacy What is the formula for the standard error of the normal
approximation to the p distribution? What is the mean of the p distribution?
19.| Statistical Literacy Is p an unbiased estimator for p when np > 5 and
ng > 5? Recall that a statistic is an unbiased estimator of the corresponding
parameter if the mean of the sampling distribution equals the parameter
in question.
te
20.| Basic Computation: p Distribution Suppose we have a binomial experi-
ment in which success is defined to be a particular quality or attribute that
interests us.
33 and p = 0.21. Can we approximate the p distribution by
(a) Suppose n =
a normal distribution? Why? What are the values of u, and o;?
(b) Suppose n =
tion by a normal distribution? Why or why not?
(c) Suppose n = 48 and p = 0.15. Can we approximate the p distribution by
a normal distribution? Why? What are the values of u; and o;?
25 and p
0.15. Can we safely approximate the p distribu-
||
Basic Computation: p Distribution Suppose we have a binomial experiment in
which success is defined to be a particular quality or attribute that interests us.
(a) Suppose n = 100 and p
bution by a normal distribution? Why? Compute
(b) Suppose n =
tion by a normal distribution? Why or why not?
21.
0.23. Can we safely approximate the p distri-
and
Op.
20 and p = 0.23. Can we safely approximate the p distribu-
PART II SUMMARY
In this part, we studied sampling distributions. We also looked at the normal
approximation to the binomial distribution. The Chapter Review has a summary of
the specific topics of this part, as well as Important Words and Symbols.
Part II Chapter Review Problems: 4, 7, 8, 9, 10, 15, 17, 21, 22, 23, 24, 25, 26.
ngage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-208](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff59662fb-eaec-4b3d-a1b9-c848915bfa7b%2F8f9a2a3c-0d97-4bfb-a82f-004c62af6df4%2Fy7xz0eri_processed.jpeg&w=3840&q=75)
Transcribed Image Text:S AND SAMPLING DISTRIBUTIONS
15.
Airline Flights: No-Shows Based on long experience, an airline has found
that about 6% of the people making reservations on a flight from Miami to
Denver do not show up for the flight. Suppose the airline overbooks this flight
by selling 267 ticket reservations for an airplane with only 255 seats.
(a) What is the probability that a person holding a reservation will show up
for the flight?
X-
(b) Let n =
267 represent the number of ticket reservations. Let r represent
the number of people with reservations who show up for the flight. Which
expression represents the probability that a seat will be available for
everyone who shows up holding a reservation?
P(255 < r); P(r < 255); P(r < 267); P(r = 255)
(c) Use the normal approximation to the binomial distribution and part (b) to
answer the following question: What is the probability that a seat will be
available for every person who shows up holding a reservation?
16.
General: Approximations We have studied two approximations to the
binomial, the normal approximation and the Poisson approximation
(See Section 5.4). Write a brief but complete essay in which
and summarize the conditions under which each approximation would be
used, the formulas involved, and the assumptions made for each approxima-
tion. Give details and examples in your essay. How could you apply these
statistical methods in your everyday life?
on,
you
discuss
17.
Statistical Literacy Under what conditions is it appropriate to use a normal
distribution to approximate the p distribution?
18.| Statistical Literacy What is the formula for the standard error of the normal
approximation to the p distribution? What is the mean of the p distribution?
19.| Statistical Literacy Is p an unbiased estimator for p when np > 5 and
ng > 5? Recall that a statistic is an unbiased estimator of the corresponding
parameter if the mean of the sampling distribution equals the parameter
in question.
te
20.| Basic Computation: p Distribution Suppose we have a binomial experi-
ment in which success is defined to be a particular quality or attribute that
interests us.
33 and p = 0.21. Can we approximate the p distribution by
(a) Suppose n =
a normal distribution? Why? What are the values of u, and o;?
(b) Suppose n =
tion by a normal distribution? Why or why not?
(c) Suppose n = 48 and p = 0.15. Can we approximate the p distribution by
a normal distribution? Why? What are the values of u; and o;?
25 and p
0.15. Can we safely approximate the p distribu-
||
Basic Computation: p Distribution Suppose we have a binomial experiment in
which success is defined to be a particular quality or attribute that interests us.
(a) Suppose n = 100 and p
bution by a normal distribution? Why? Compute
(b) Suppose n =
tion by a normal distribution? Why or why not?
21.
0.23. Can we safely approximate the p distri-
and
Op.
20 and p = 0.23. Can we safely approximate the p distribu-
PART II SUMMARY
In this part, we studied sampling distributions. We also looked at the normal
approximation to the binomial distribution. The Chapter Review has a summary of
the specific topics of this part, as well as Important Words and Symbols.
Part II Chapter Review Problems: 4, 7, 8, 9, 10, 15, 17, 21, 22, 23, 24, 25, 26.
ngage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-208
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