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# On 100 different days, a traffic engineer counts the

ISBN: 9780073401331 38

## Solution for problem 9E Chapter 2.4

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition

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Problem 9E

On 100 different days, a traffic engineer counts the number of cars that pass through a certain intersection between 5 p.m. and 5:05 p.m. The results are presented in the following table.

 Number of Cars Number of Days Proportion of Days 0 36 0.36 1 28 0.28 2 15 0.15 3 10 0.10 4 7 0.07 5 4 0.04

a. Let X be the number of cars passing through the intersection between 5 P.M. and 5:05 P.M. on a randomly chosen day. Someone suggests that for any positive integer x, the probability mass function of X is p1(x) = (0.2) (0.8) x. Using this function, compute P(X = x) for values of x from 0 through 5 inclusive.

b. Someone else suggests that for any positive integer x, the probability mass function is p2(x) = (0.4)(0.6)x. Using this function, compute P(X  =  x) for values of x from 0 through 5 inclusive.

c. Compare the results of parts (a) and (b) to the data in the table. Which probability mass function appears to be the better model? Explain.

d. Someone says that neither of the functions is a good model since neither one agrees with the data exactly. Is this right? Explain.

Step-by-Step Solution:

Step 1 of 5 :

Given, a traffic engineer counts the number of cars that pass through a certain intersection between 5.pm and 5:05 pm. On 100 different days

 Number of cars Number of days Proportion of days 0 36 0.36 1 28 0.28 2 15 0.15 3 10 0.10 4 7 0.07 5 4 0.04

Step 2 of 5 :

Where X be the number of cars passing through the intersection between 5 P.M. and 5:05 P.M.

For any positive integer x, the probability mass function of X is

(x) = (0.2) (0.8.

The claim is to compute P(X = x) for values of x from 0 through 5 inclusive

Then,  (0) = (0.2) (0.8.

= 0.2

(1) = (0.2) (0.8.

= 0.16

(2) = (0.2) (0.8.

= 0.128

(3) = (0.2) (0.8.

= 0.1024

(4) = (0.2) (0.8.

= 0.0819

(5) = (0.2) (0.8.

= 0.0655

Step 3 of 5 :

b)

For any positive integer x, the probability mass function of X is

(x) = (0.4) (0.6.

The claim is to compute P(X = x) for values of x from 0 through 5 inclusive

Then,  (0) = (0.4) (0.6.

= 0.4

(1) = (0.4) (0.6.

= 0.24

(2) = (0.4) (0.6.

= 0.144

(3) = (0.4) (0.6.

= 0.0864

(4) = (0.4) (0.6.

= 0.0518

(5) = (0.4) (0.6.

= 0.0311

Step 4 of 5

Step 5 of 5

##### ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 9E from 2.4 chapter was answered, more than 408 students have viewed the full step-by-step answer. The answer to “On 100 different days, a traffic engineer counts the number of cars that pass through a certain intersection between 5 p.m. and 5:05 p.m. The results are presented in the following table. Number of Cars Number of DaysProportion of Days0360.361280.282150.153100.10470.07540.04a. Let X be the number of cars passing through the intersection between 5 P.M. and 5:05 P.M. on a randomly chosen day. Someone suggests that for any positive integer x, the probability mass function of X is p1(x) = (0.2) (0.8) x. Using this function, compute P(X = x) for values of x from 0 through 5 inclusive.________________b. Someone else suggests that for any positive integer x, the probability mass function is p2(x) = (0.4)(0.6)x. Using this function, compute P(X = x) for values of x from 0 through 5 inclusive.________________c. Compare the results of parts (a) and (b) to the data in the table. Which probability mass function appears to be the better model? Explain.________________d. Someone says that neither of the functions is a good model since neither one agrees with the data exactly. Is this right? Explain.” is broken down into a number of easy to follow steps, and 179 words. The full step-by-step solution to problem: 9E from chapter: 2.4 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: function, days, Probability, mass, cars. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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