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Chapter 4: Q.129 (page 299)

Find the probability that her cats will wake her up no more than five times next week.

a.0.5000b.0.9329c.0.0378d.0.0671

Short Answer

Expert verified

The answer is Option (d) is the correct answerP(X≤5)=0.0571.

Step by step solution

01

Introduction 

Probability is a discipline of mathematics concerned with numerical explanations of the likelihood of an event occurring or the truth of a claim. The probability of an event is a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty, broadly speaking.

02

Given

Mrs. Plum's cats wake her up on average 10 times every week.

03

Formula used 

This is the formula we used P(X=x)=e-λ×λxx!.

04

Explanation 

P(X≤5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)

+P(X=5)

P(X≤5)=e-10×1000!+e-10×1011!+e-10×1022!+e-10×1033!+e-10×1044!+e-10×1055!

it is near about given P(X≤5)=0.057085≈0.0571

so, the final answer we have ,

We can easily see that Option D is right based on the calculations above.

P(X≤5)=0.0571.

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Most popular questions from this chapter

Suppose that the probability that an adult in America will watch the Super Bowl is 40%. Each person is considered independent. We are interested in the number of adults in America we must survey until we find one who will watch the Super Bowl.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. How many adults in America do you expect to survey until you find one who will watch the Super Bowl?

e. Find the probability that you must ask seven people.

f. Find the probability that you must ask three or four people

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a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. What is the probability that at least eight have adequate earthquake supplies?

e. Is it more likely that none or that all of the residents surveyed will have adequate earthquake supplies? Why?

f. How many residents do you expect will have adequate earthquake supplies?

Define the random variable X.

A customer service center receives about ten emails every half-hour. What is the probability that the customer service center receives more than four emails in the next six minutes? Use the TI-83+ or TI-84 calculator to find the answer.

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