Beginning Statistics, 2nd Edition
Beginning Statistics, 2nd Edition
2nd Edition
ISBN: 9781932628678
Author: Carolyn Warren; Kimberly Denley; Emily Atchley
Publisher: Hawkes Learning Systems
Question
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Chapter 5.3, Problem 15E
To determine

The probability of the given scenario.

Expert Solution & Answer
Check Mark

Answer to Problem 15E

Solution:

The value of the required probability is 0.258760

Explanation of Solution

Given Information:

Assume a random variable X follows Poisson distribution with λ = 9.60.

Formula used:

For a Poisson random variable X, the probability of getting successes in a given interval is given by:

P(X=x)=eλλxx!

P(Xr)=1P(X<r)=1(P(X=0)+P(X=1)+...+P(X=r1))

Where,

X is the number of successes occurred

λ is the mean number of successes in a each interval.

Calculation:

Substitute 12 for r and 9.60 for λ in the greater than formula mentioned above,

P(X12)=1P(X<12)=1P(X11)=P(X=0)+P(X=1)+P(X=2)+............+P(X=6)+P(X=7)+..........+P(X=11)

Substitute 0 for r, and 9.60 for λ in the formula of P(X=r) to calculate P(X=0).

P(X=0)=e9.609.6000!=0.000067729

Substitute 1 for r, and 9.60 for λ in the formula of P(X=r) to calculate P(X=1).

P(X=1)=e9.609.601=0.00065019

Substitute 2 for r, and 9.60 for λ in the formula of P(X=r) to calculate P(X=2)

P(X=2)=e9.609.6022!=0.00006772×92.162=0.0031209

Substitute 3 for r, and 9.60 for λ in the formula of P(X=r) to calculate P(X=3)

P(X=3)=e9.609.6033!=0.00006772×9.6036=0.009987

Substitute 4 for r, and 9.60 for λ in the formula of P(X=r) to calculate P(X=4)

P(X=4)=e9.609.6044!=0.00006772×9.60424=0.0239688

Substitute 5 for r, and 9.60 for λ in the formula of P(X=r) to calculate P(X=5)

P(X=5)=e9.609.6055!=0.00006772×9.605120=0.046020

Substitute 6 for r, and 9.60 for λ in the formula of P(X=r) to calculate P(X=6)

P(X=6)=e9.609.6066!=0.00006772×9.606720=0.073632

Substitute 7 for r, and 9.60 for λ in the formula of P(X=r) to calculate P(X=7)

P(X=7)=e9.609.6077!=0.00006772×9.6075040=0.1009813

Substitute 8 for r, and 9.60 for λ in the formula of P(X=r) to calculate P(X=8)

P(X=8)=e9.609.6088!=0.00006772×9.6088!=0.121177

Substitute 9 for r, and 9.60 for λ in the formula of P(X=r) to calculate P(X=9)

P(X=9)=e9.609.6099!=0.00006772×9.6099!=0.129256

Substitute 10 for r, and 9.60 for λ in the formula of P(X=r) to calculate P(X=10)

P(X=10)=e9.609.601010!=0.00006772×9.601010!=0.124085

Substitute 11 for r, and 9.60 for λ in the formula of P(X=r) to calculate P(X=11)

P(X=11)=e9.609.601111!=0.00006772×9.601111!=0.10829

Add all the values of

P(X=0),P(X=1)....,P(X=11) then,

P(X12)=1P(X<12)=1P(X11)=P(X=0)+P(X=1)+P(X=2)+............+P(X=6)+P(X=7)+..........+P(X=11)=0.2588

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Chapter 5 Solutions

Beginning Statistics, 2nd Edition

Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.2 - Prob. 1ECh. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - Prob. 13ECh. 5.2 - Prob. 14ECh. 5.2 - Prob. 15ECh. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Prob. 19ECh. 5.2 - Prob. 20ECh. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Prob. 23ECh. 5.2 - Prob. 24ECh. 5.2 - Prob. 25ECh. 5.3 - Prob. 1ECh. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Prob. 6ECh. 5.3 - Prob. 7ECh. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Prob. 11ECh. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.CR - Prob. 1CRCh. 5.CR - Prob. 2CRCh. 5.CR - Prob. 3CRCh. 5.CR - Prob. 4CRCh. 5.CR - Prob. 5CRCh. 5.CR - Prob. 6CRCh. 5.CR - Prob. 7CRCh. 5.CR - Prob. 8CRCh. 5.CR - Prob. 9CRCh. 5.CR - Prob. 10CRCh. 5.CR - Prob. 11CRCh. 5.CR - Prob. 12CRCh. 5.CR - Prob. 13CRCh. 5.P - Prob. 1PCh. 5.P - Prob. 2PCh. 5.P - Prob. 3PCh. 5.P - Prob. 4PCh. 5.P - Prob. 5PCh. 5.P - Prob. 6PCh. 5.P - Prob. 7PCh. 5.P - Prob. 8PCh. 5.P - Prob. 9PCh. 5.P - Prob. 10PCh. 5.P - Prob. 11PCh. 5.P - Prob. 12PCh. 5.P - Prob. 13PCh. 5.P - Prob. 14PCh. 5.P - Prob. 15PCh. 5.P - Prob. 16PCh. 5.P - Prob. 17P
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