Question

An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is given. y | 0 1 2 3 p(y) | 0.40 0.35 0.15 0.10 (a) What is the probability that among 25 randomly chosen such individuals, at least 15 have no citations? (Round your answer to three decimal places.) (b) What is the probability that among 25 randomly chosen such individuals, fewer than half have at least one citation? (Round your answer to three decimal places.) (c) What is the probability that among 25 randomly chosen such individuals, the number that have at least one citation is between 10 and 15, inclusive? ("Between a and b, inclusive" is equivalent to (a ? X ? b)). Round your answer to three decimal places. You may need to use the appropriate table in the Appendix of Tables to answer this question.

          An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is given.
y | 0 1 2 3
p(y) | 0.40 0.35 0.15 0.10
(a) What is the probability that among 25 randomly chosen such individuals, at least 15 have no citations? (Round your answer to three decimal places.)
(b) What is the probability that among 25 randomly chosen such individuals, fewer than half have at least one citation? (Round your answer to three decimal places.)
(c) What is the probability that among 25 randomly chosen such individuals, the number that have at least one citation is between 10 and 15, inclusive? ("Between a and b, inclusive" is equivalent to (a ? X ? b)). Round your answer to three decimal places.
You may need to use the appropriate table in the Appendix of Tables to answer this question.

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An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is given.
y | 0 1 2 3
p(y) | 0.40 0.35 0.15 0.10
(a) What is the probability that among 25 randomly chosen such individuals, at least 15 have no citations? (Round your answer to three decimal places.)
(b) What is the probability that among 25 randomly chosen such individuals, fewer than half have at least one citation? (Round your answer to three decimal places.)
(c) What is the probability that among 25 randomly chosen such individuals, the number that have at least one citation is between 10 and 15, inclusive? ("Between a and b, inclusive" is equivalent to (a ? X ? b)). Round your answer to three decimal places.
You may need to use the appropriate table in the Appendix of Tables to answer this question.

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Ahmet Yavas

09/28/2022

Step 1

From the given pmf, the probability \( P(Y = 0) = 0.40 \). Show more…

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An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is given. y | 0 1 2 3 p(y) | 0.40 0.35 0.15 0.10 (a) What is the probability that among 25 randomly chosen such individuals, at least 15 have no citations? (Round your answer to three decimal places.) (b) What is the probability that among 25 randomly chosen such individuals, fewer than half have at least one citation? (Round your answer to three decimal places.) (c) What is the probability that among 25 randomly chosen such individuals, the number that have at least one citation is between 10 and 15, inclusive? ("Between a and b, inclusive" is equivalent to (a ≤ X ≤ b)). Round your answer to three decimal places. You may need to use the appropriate table in the Appendix of Tables to answer this question.

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00:01 This is the given probability mass function table here.

00:06 And the number of, so let's take a look at for part a, the problem that among 25 random niches in individuals.

00:13 So the sample size, which is given as 25 here.

00:17 So at least 15 have no citations.

00:19 So the probability of no citation, which is when y is equal to 0, 0 .40 here.

00:28 So that means the q value, which is 1 minus p here, that would be 1 minus 0 .40, that would be 0 .60 here.

00:39 So we have to select at least 25 hand no side tension.

00:44 So at this step, we're going to use the binomial distribution.

00:47 Let's say x be the random variable for this binomial distribution.

00:51 The n value here is 25 and the probability of the success, which is 0 .40 here.

00:56 So if it says at least 15, so the number of people should be 16, 15, 16, and 17 and so forth.

01:05 So the probability of the random variable x, which is greater than or equal to 15.

01:11 So i can just write this expression as the total probability, which is one, and the exclude part, which is x is less than or equal to 14.

01:22 So we can just get this value by using the normal and not normal.

01:28 So this is binom cdf function.

01:32 We can just use binom cdf application for the graphic display calculator.

01:38 So for the binom cdf, i'm going to just press the bottom second here and the distribution.

01:42 And there is binom cdf here.

01:45 Here we go.

01:46 So what we have to put, we have to put the total number of people here, which is 25.

01:50 And the probability value, which is 0 .4d, and the x value here, which is the 14 is included.

01:57 So i'm going to put the 14 here.

01:59 So i'm going to just write this number.

02:01 This is 25, and then 0 .40, and then 14...

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