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Peck/Olsen/Devore-Intro to Stat & Data Analysis 3e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 33 / 35

Due : Sunday, January 27, 2030 23:30 EST

Last Saved : n/a Saving...  ()

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  • Instructions

    Create your course assignments by selecting questions from our bank of end-of-section questions, as well as enhanced interactive examples with videos.

    Students can view and hear additional instruction through the 2-5 minute Watch It links. Students will also find helpful links to online excerpts from their textbook, online-live help, tutorials, and videos.

    Read It - relevant textbook pages

    Watch It - videos of worked examples

    Practice It - interactive examples

    Chat About It - online, live help

    While doing their homework, students can link to the relevant interactive examples from the book and work through them again and again for additional practice before answering the question.

    Students can view and hear additional instruction through the 2-5 minute Watch It links. Students will also find helpful links to online excerpts from their textbook, online live tutoring by statistics experts, and videos with stepped-out solutions.
    • relevant textbook pages
    • videos of stepped-out solutions
    • interactive examples
    • online, live help
    In this assignment we present several textbook question types found in Chapter 7 in Introduction to Statistics and Data Analysis 3/e by Roxy Peck, Chris Olsen, and Jay L. Devore, published by Thomson-Brooks/Cole.

    Questions 1 through 4 are randomized end-of-section questions taken directly from the textbook. The correct answer is displayed after answers are submitted for this sample assignment.

    Questions 5 and 6 are Active Examples taken directly from Examples 7.8 and 7.15 in the text. Students will have greater understanding of the material by actively working through the problem than passively reading through them. This demo assignment allows many submissions and allows you to try another version of the same question for practice.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

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1. –/8 points PODStat3 7.E.009. My Notes
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Let y denote the number of broken eggs in a randomly selected carton of one dozen "store brand" eggs at a certain market. Suppose that the probability distribution of y is as follows.
y01234
p(y).64.18.10.05?
(a) Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)?

(b) How would you interpret p(1) = .18?
    


(c) Calculate P(y ≤ 2), the probability that the carton contains at most two broken eggs.

Interpret this probability.
    


(d) Calculate P(y < 2), the probability that the carton contains fewer than two broken eggs.

Why is this smaller than the probability in part (c)?
    


(e) What is the probability that the carton contains exactly 10 unbroken eggs? (Hint: What is the corresponding value of y?)


(f) What is the probability that at least 10 eggs are unbroken?


You may need to use the appropriate table in Appendix A to answer this question.

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2. –/4 points PODStat3 7.E.040. My Notes
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–/4
 
An appliance dealer sells three different models of upright freezers having 14.5, 16.9, and 19.1 cubic feet of storage space. Let x = the amount of storage space purchased by the next customer to buy a freezer. Suppose that x has the following probability distribution.
xp(x)
14.5.2
16.9.5
19.1.3
(a) Calculate the mean and standard deviation of x. (Round the answers to three decimal places.)
Mean = cu. ft
Standard deviation = cu. ft

(b) If the price of the freezer depends on the size of the storage space, x, such that Price = 25x - 8.5, what is the mean value of the variable Price paid by the next customer?
Mean = $

(c) What is the standard deviation of the price paid? (Round the answer to the nearest cent.)
Standard deviation = $


You may need to use the appropriate table in Appendix A to answer this question.
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3. –/6 points PODStat3 7.E.041. My Notes
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–/6
 
To assemble a piece of furniture, a wood peg must be inserted into a predrilled hole. Suppose that the diameter of a randomly selected peg is a random variable with mean 0.35 in. and standard deviation 0.009 in. and that the diameter of a randomly selected hole is a random variable with mean 0.354 in. and standard deviation 0.004 in. Let x1 denote peg diameter, and let x2 denote hole diameter.
(a) Why would the random variable y, defined as y = x2 - x1, be of interest to the furniture manufacturer?
    


(b) What is the mean value of the random variable y?
Mean = in.

(c) Assuming that x1 and x2 are independent, what is the standard deviation of y? (Round the answer to three decimal places.)
Standard deviation = in.
(d) Is it reasonable to think that x1 and x2 are independent?
    

Explain. (Select all that apply.)


(e) Based on your answers to parts (b) and (c), do you think that finding a peg that is too big to fit in the predrilled hole would be a relatively common or a relatively rare occurrence? Explain.
    


You may need to use the appropriate table in Appendix A to answer this question.

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4. –/3 points PODStat3 7.E.062. My Notes
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–/3
 
Suppose that 5% of cereal boxes contain a prize and the other 95% contain the message, "Sorry, try again." Consider the random variable x, where x = number of boxes purchased until a prize is found. (Round all answers to four decimal places.)
(a) What is the probability that at most three boxes must be purchased?
P(at most three boxes) =

(b) What is the probability that exactly four boxes must be purchased?
P(exactly four boxes) =

(c) What is the probability that more than four boxes must be purchased?
P(more than four boxes) =


You may need to use the appropriate table in Appendix A to answer this question.
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5. –/7 points PODStat3 7.AE.008. My Notes
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Example 7.8Exam Attempts
Individuals applying for a certain license are allowed up to four attempts to pass the licensing exam. Let x denote the number of attempts made by a randomly selected applicant. The probability distribution of x is as follows.
x 12 34
p(x) 0.15 0.2 0.2 0.45
Thus x has mean value as given below.
μx = sum_(x = 1text(,)2text(,)3text(,)4) (x)p(x)
= (1)p(1) + (2)p(2) + ( )p(3) + ( )p(4)
= (1)( ) + (2)( ) + ( )(0.2) + ( )(0.45)
= 0.15 + 0.4 + 0.6 + 1.8
=


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6. –/7 points PODStat3 7.AE.015. My Notes
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Example 7.15Combining Exam Subscores
A nationwide standardized exam consists of a multiple-choice section and a free-response section. For each section, the mean and standard deviation are reported to be as follows.

Mean Standard
Deviation
Multiple choice 41 7
Free response 41 7


Let's define x1 and x2 as the multiple-choice score and the free-response score, respectively, of a student selected at random from those taking the exam. We are also interested in the variable y = total score. Suppose that the total score is computed as y = x1 + 2x2. What are the mean and standard deviation of y?

Because y = x1 + 2x2 is a combination of x1 and x2, the mean of y is computed as follows.
µy = µx1 + 2x2
= µx1 + µx2
= 41 + ( )
=
What about the variance and standard deviation of y? To use the rule for variance of combinations, x1 and x2 must be . It is unlikely that the value of x1 (a student's multiple choice score) would be unrelated to the value of x2 (the same student's free response score), because it seems probable that students who score well on one section of the exam will also tend to score well on the other section. Therefore, it would not be appropriate to calculate the variance and standard deviation from the given information.


You may need to use the appropriate table in Appendix A to answer this question.
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