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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. 65 (page 382)

The mean of $T$ is
(a) $110$
(b) $140$
(c) $180$
(d) $195$
(e) $250$

Short Answer

Expert verified

The mean of $T$ is option (c) $180 .$

Step by step solution

01

Concept Introduction

A mean is a measurement of center of gravity in a probability distribution, along with mean, median, and mode. In statistics, it is a measure of central tendency.

02

Explanation

Given:

$μ_{X} = 110$

$σ_{X} = 10$

$μ_{Y} = 140$

$σ_{Y} = 12$

Property mean and variance (if $X$ and $Y$ are independent):

localid="1649859475011" $μ_{a X + b Y} = (a μ_{X} + b μ_{Y}) σ_{a X + b Y}^{2} = (a^{2} μ_{X}^{2} + b^{2} μ_{Y}^{2})$

The obtained results are:

localid="1649859480196" $μ_{X + Y / 2} = μ_{X} + \frac{1}{2} μ_{Y} = 110 + \frac{1}{2} (140) = 180$

localid="1649859485292" $σ_{X + Y / 2} = \sqrt{σ_{X}^{2} + \frac{1}{2^{2}} σ_{X_{2}}^{2}} = \sqrt{(10^{2} + \frac{1}{4} 12^{2})} \approx 11.66$

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Most popular questions from this chapter

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 $X$ and $Y$ are as follows:

Deﬁne $T = X + Y$ .

Find and interpret $μ T$ .

Ten lines in the table contain $400$ digits. The count of $0$ s in these lines is approximately Normal with

(a) mean $40$ ; standard deviation $36 .$

(b) mean $40$ ; standard deviation $19 .$

(c) mean $40$ ; standard deviation $6 .$

(d) mean $36$ ; standard deviation $6 .$

(e) mean $10$ ; standard deviation $19 .$

Running a mile A study of $12, 000$ able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean $7.11$ minutes and standard deviation $0.74$ minute. Choose a student at random from this group and call his time for the mile $Y$ . Find $P (Y < 6)$ and interpret the result. Follow the four-step process.

81. Random digit dialing When an opinion poll calls residential telephone numbers at random, only $20 %$ of the calls reach a live person. You watch the random digit dialing machine make $15$ calls. Let $X =$ the number of calls that reach a live person.
(a) Find and interpret $μ X$ .
(b) Find and interpret $σ X$ .

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 $μ_{X}$ . Interpret this value in context.

2. Find localid="1649452775386" $σ_{X}$ . Interpret this value in context.

See all solutions

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