Decide whether you can use the normal distribution to approximate the binomial distribution. If you​ can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you​ cannot, explain why and use the binomial distribution to find the indicated probabilities.   A survey of adults found that 7​% say their favorite sport is auto racing. You randomly select 300 adults and ask them to name their favorite sport. Complete parts​ (a) through​ (d).

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
Decide whether you can use the normal distribution to approximate the binomial distribution. If you​ can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you​ cannot, explain why and use the binomial distribution to find the indicated probabilities.
 
A survey of adults found that 7​% say their favorite sport is auto racing. You randomly select 300 adults and ask them to name their favorite sport. Complete parts​ (a) through​ (d).
Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below.
A. No, because np < 5.
B. Yes, because both np >5 and nq 2 5.
O C. No, because ng < 5.
(a) Find the probability that the number of people who say auto racing is their favorite sport is at most 26.
(Round to four decimal places as needed.)
Sketch the graph of the normal distribution with the indicated probability shaded.
O A.
О в.
OC.
D.
H=21
H=21
H=21
The normal distribution cannot be used to
approximate the binomial distribution.
26
36
26
36
26
36
(b) Find the probability that the number of people who say auto racing is their favorite sport is more than 29.
(Round to four decimal places as needed.)
Sketch the graph of the normal distribution with the indicated probability shaded.
O A.
В.
D.
H=21
H=21
H=21
The normal distribution cannot be used to
approximate the binomial distribution.
29 36
29 36
29 36
(c) Find the probability that the number of people who say auto racing is their favorite sport is between 18 and 23, inclusive.
(Round to four decimal places as needed.)
Transcribed Image Text:Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below. A. No, because np < 5. B. Yes, because both np >5 and nq 2 5. O C. No, because ng < 5. (a) Find the probability that the number of people who say auto racing is their favorite sport is at most 26. (Round to four decimal places as needed.) Sketch the graph of the normal distribution with the indicated probability shaded. O A. О в. OC. D. H=21 H=21 H=21 The normal distribution cannot be used to approximate the binomial distribution. 26 36 26 36 26 36 (b) Find the probability that the number of people who say auto racing is their favorite sport is more than 29. (Round to four decimal places as needed.) Sketch the graph of the normal distribution with the indicated probability shaded. O A. В. D. H=21 H=21 H=21 The normal distribution cannot be used to approximate the binomial distribution. 29 36 29 36 29 36 (c) Find the probability that the number of people who say auto racing is their favorite sport is between 18 and 23, inclusive. (Round to four decimal places as needed.)
Sketch the graph of the normal distribution with the indicated probability shaded.
O A.
В.
OC.
OD.
H=21
H=21
H=21
The normal distribution cannot be used to
approximate the binomial distribution.
18 23
36
18 23
36
18 23
36
(d) Identify any unusual events. Explain.
A. The event in part (b) is unusual because its probability is less than 0.05.
B. The event in part (c) is unusual because its probability is less than 0.05.
C. The event in part (a) is unusual because its probability is less than 0.05.
D. There are no unusual events, because all of the probabilities are greater than 0.05.
-------
--------
-----------
Transcribed Image Text:Sketch the graph of the normal distribution with the indicated probability shaded. O A. В. OC. OD. H=21 H=21 H=21 The normal distribution cannot be used to approximate the binomial distribution. 18 23 36 18 23 36 18 23 36 (d) Identify any unusual events. Explain. A. The event in part (b) is unusual because its probability is less than 0.05. B. The event in part (c) is unusual because its probability is less than 0.05. C. The event in part (a) is unusual because its probability is less than 0.05. D. There are no unusual events, because all of the probabilities are greater than 0.05. ------- -------- -----------
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 4 images

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman