PRACT STAT W/ ACCESS 6MO LOOSELEAF
PRACT STAT W/ ACCESS 6MO LOOSELEAF
4th Edition
ISBN: 9781319215361
Author: BALDI
Publisher: Macmillan Higher Education
Question
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Chapter 12, Problem 12.18AYK

(a)

To determine

To use technology to find the cumulative probabilities of Xequals 0,1,2,3, to 15 .

(a)

Expert Solution
Check Mark

Answer to Problem 12.18AYK

    Xcumulative probabilities
    10.00394
    20.017364
    30.051819
    40.118145
    50.220287
    60.351369
    70.49556
    80.634343
    90.75308
    100.844508
    110.908507
    120.949573
    130.973897
    140.987275
    150.994143

Explanation of Solution

It is given in the question that the CDC receives reports of 7.7 cases of typhoid fever per week, on average, from all over the United States, although most cases were acquired during international travel. Let Xbe the number of cases of typhoid cases received. Xhave a Poisson distribution with average of 7.7 cases of typhoid fever per week. To find the cumulative probabilities of X equals 0,1,2,3, to 15 we will use excel function. The excel function is:

  =POISSON.DIST(x,mean, cumulative)

In the cumulative, the FALSE gives the exact value and TRUE gives the less than value.

Thus, the calculation is as:

    Xcumulative probabilities
    1=POISSON.DIST(AJ116,7.7,TRUE)
    2=POISSON.DIST(AJ117,7.7,TRUE)
    3=POISSON.DIST(AJ118,7.7,TRUE)
    4=POISSON.DIST(AJ119,7.7,TRUE)
    5=POISSON.DIST(AJ120,7.7,TRUE)
    6=POISSON.DIST(AJ121,7.7,TRUE)
    7=POISSON.DIST(AJ122,7.7,TRUE)
    8=POISSON.DIST(AJ123,7.7,TRUE)
    9=POISSON.DIST(AJ124,7.7,TRUE)
    10=POISSON.DIST(AJ125,7.7,TRUE)
    11=POISSON.DIST(AJ126,7.7,TRUE)
    12=POISSON.DIST(AJ127,7.7,TRUE)
    13=POISSON.DIST(AJ128,7.7,TRUE)
    14=POISSON.DIST(AJ129,7.7,TRUE)
    15=POISSON.DIST(AJ130,7.7,TRUE)

The result will be as:

    Xcumulative probabilities
    10.00394
    20.017364
    30.051819
    40.118145
    50.220287
    60.351369
    70.49556
    80.634343
    90.75308
    100.844508
    110.908507
    120.949573
    130.973897
    140.987275
    150.994143

(b)

To determine

To find out what is the probability that the CDC receives reports of more than 15 cases of typhoid fever next month and if this happen what would you conclude.

(b)

Expert Solution
Check Mark

Answer to Problem 12.18AYK

  0.003346 .

Explanation of Solution

It is given in the question that the CDC receives reports of 7.7 cases of typhoid fever per week, on average, from all over the United States, although most cases were acquired during international travel. Let Xbe the number of cases of typhoid cases received. Xhave a Poisson distribution with average of 7.7 cases of typhoid fever per week. To find the probability that the CDC receives reports of more than 15 cases of typhoid fever next month we will use excel function. The excel function is:

  =POISSON.DIST(x,mean, cumulative)

In the cumulative, the FALSE gives the exact value and TRUE gives the less than value.

Thus, the calculation is as:

  P(X>15)=1P(X<15)

    P(X>15)==1-POISSON.DIST(15,7.7,TRUE)

The result is as:

    P(X>15)=0.005857

Thus, the probability that the CDC receives reports of more than 15 cases of typhoid fever next monthis 0.003346 . If this happens that then we conclude that the city have most cases for typhoid fever and it will be increasing more and the people must take precaution for the same by avoiding unhygienic foods but the probability calculated above is less so the chance for this is to happen is low.

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