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Chapter 6: Q.12 (page 354)

Kids and toys Refer to Exercise 4. Calculate the mean of the random variable X and interpret this result in context.

Short Answer

Expert verified

On average there are 2.68 toys that are played with.

Step by step solution

01

Given Information

The probability distribution of the number X of toys played with by a randomly selected subject is as follows:

02

Explanation

The expected value is calculated by multiplying each possibility by its probability:

E(X)=∑xP(x)=0×0.03+1×0.16+2×0.30+3×0.23+4×0.17+5×0.11=2.68

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Most popular questions from this chapter

Refer to the previous Check Your Understanding (page 390 ) about Mrs. Desai's special multiple-choice quiz on binomial distributions. We defined X=the number of Patti's correct guesses.

1. Find μX. Interpret this value in context.

2. Find localid="1649452775386" σX. Interpret this value in context.

Fire insurance Suppose a homeowner spends \(300for a home insurance policy that will pay out \)200,000if the home is destroyed by fire. Let Y=the profit made by the company on a single policy. From previous data, the probability that a home in this area will be destroyed by fire is 0.0002.

(a) Make a table that shows the probability distribution of Y.

(b) Compute the expected value of Y. Explain what this result means for the insurance company

The standard deviation of Tis

(a)22

(b) 16

(c)15.62

(d)11.66

(e)4

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let X= the number of cars sold and Y= the number of cars leased during the first hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

Define T=X+Y.

Find and interpret μT.

83. Random digit dialing Refer to Exercise 81. Let Y= the number of calls that don’t reach a live person.

(a) Find the mean of Y. How is it related to the mean of X? Explain why this makes sense.
(b) Find the standard deviation of Y.How is it related to the standard deviation of X? Explain why this makes sense

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