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Chapter 4: Q.4.54 (page 167)

Suppose that the average number of cars abandoned weekly on a certain highway is 2.2. Approximate the probability that there will be

(a) no abandoned cars in the next week;

(b) at least abandoned cars in the next week.

Short Answer

Expert verified

The probability that there will be no abandoned cars in the next week is0.1108.

The probability that there will be at least 2abandoned cars in the next week is0.645.

Step by step solution

01

Given Information (Part-a)

Given in the question that the average number of cars abandoned weekly on a certain highway is2.2. The probability that there will be no abandoned cars in the next week.

02

Solution of the Problem (Part-a)

Given 位=2.2

P(X=0)=e-位(位)00!

We get,

=e-2.22.200!

=0.1108.

03

Final Answer (Part-a)

The probability that there will be no abandoned cars in the next week is0.1108.0.1108.

04

Given Information (Part-b)

Given in the question that the average number of cars abandoned weekly on a certain highway is 2.2.The probability that there will be at least 2abandoned cars in the next week.

05

Solution of the Problem (Part-b)

Given位=2.2

P(X鈮�2)=1-P(X鈮�1)

=1-[P(X=0)+P(X=1)]

We get,

=1-[0.1108+0.2438]

=0.645.

06

Final Answer (Part-b)

The probability that there will be at least 2 abandoned cars in the next week is0.645.

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