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 9% 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).
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 9% 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).
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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 9% 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).
Transcribed Image Text:Determine whether a normal distribution can be used to approximate the binomial distribution. Choose the correct answer below.
A. No, because nq < 5.
B. Yes, because both np >5 and nq 2 5.
O C. No, because np <5.
(a) Find the probability that the number of people who say auto racing is their favorite sport is at most 33.
(Round to four decimal places as needed.)
Sketch the graph of the normal distribution with the indicated probability shaded.
O A.
В.
С.
D.
The normal distribution cannot be used to
H=27
µ =27
µ =27
approximate the binomial distribution.
10
33
44
10
33
44
10
33
44
(b) Find the probability that the number of people who say auto racing is their favorite sport is more than 36.
| (Round to four decimal places as needed.)
Sketch the graph of the normal distribution with the indicated probability shaded.
O A.
В.
с.
D.
The normal distribution cannot be used to
µ= 27
H=27
H=27
approximate the binomial distribution.
36 44
10
36 44
10
36 44
(c) Find the probability that the number of people who say auto racing is their favorite sport is between 24 and 29, inclusive.
(Round to four decimal places as needed.)
Transcribed Image Text:Sketch the graph of the normal distribution with the indicated probability shaded.
O A.
В.
C.
O D.
H= 27
H=27
H=27
The normal distribution cannot be used to
approximate the binomial distribution.
10
24 29
44
10
24 29
44
10
TTTT
24 29
44
(d) Identify any unusual events. Explain.
A. The event in part (c) is unusual because its probability is less than 0.05.
B. The event in part (a) is unusual because its probability is less than 0.05.
C. The event in part (b) 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.
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O O
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