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The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset Vaia Explanations$ Math

4th Edition · 809 pages

ISBN: 9781319113339

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:

$E (X) = \sum x P (x) = 0 \times 0.03 + 1 \times 0.16 + 2 \times 0.30 + 3 \times 0.23 + 4 \times 0.17 + 5 \times 0.11 = 2.68$

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Most popular questions from this chapter

19. Housing in San Jose How do rented housing units differ from units occupied by their owners? Here are the distributions of the number of rooms for owner-occupied units and renter-occupied units in San Jose,
California:

Let X = the number of rooms in a randomly selected owner-occupied unit and Y = the number of rooms in a randomly chosen renter-occupied unit.
(a) Make histograms suitable for comparing the probability distributions of X and Y. Describe any differences that you observe.
(b) Find the mean number of rooms for both types of housing unit. Explain why this difference makes sense.
(c) Find the standard deviations of both X and Y. Explain why this difference makes sense.

To introduce her class to binomial distributions, Mrs. Desai gives a 10 -item, multiple-choice quiz. The catch is, that students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class. Let $X =$ the number of Patti's correct guesses.

1. Show that $X$ is a binomial random variable.

A small ferry runs every half hour from one side of a large river to the other. The number of cars $X$ on a randomly chosen ferry trip has the probability distribution shown below. You can check that $μ_{X} = 3.87$ and $σ_{X} = 1.29$ .

(a) The cost for the ferry trip is $$ 5$ . Make a graph of the probability distribution for the random variable $M =$ money collected on a randomly selected ferry trip. Describe its shape.

(b) Find and interpret $μ_{M}$ .

(c) Compute and interpret $σ_{M}$ .

Kids and toys Refer to Exercise 4. Calculate and interpret the standard deviation of the random variable $X$ . Show your work.

Friends How many close friends do you have? An opinion poll asks this question of an SRS of $1100$ adults. Suppose that the number of close friends adults claim to have varies from person to person with mean $μ = 9$ and standard deviation $σ = 2.5$ . We will see later that in repeated random samples of size 1100, the mean response x will vary according to the Normal distribution with mean $9$ and standard deviation $0.075$ . What is role="math" localid="1649504967961" $P (8.9 \leq x \leq 9.1)$ , the probability that the sample result x estimates the population truth $μ = 9$ to within $\pm 0.1$ ?

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