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Chapter 3: Q. 6 (page 106)

Who studies more? Researchers asked the students in a large first-year college class how many minutes they studied on a typical weeknight. The back-to-back stemplot displays the responses from random samples of 30women and 30 men from the class, rounded to the nearest 10minutes. Write a few sentences comparing the male and female distributions of study time.

Short Answer

Expert verified

The velocity of car isv=5m/s.

Step by step solution

01

Part (a): Step 1: Given Information

The distance travelled by car is given asd=6m.

02

Part (a): Step 2: Explanation

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03

Part (b): Step 1: Given Information

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04

Part (b): Step 2: Explanation

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Most popular questions from this chapter

There are two Certified Public Accountants in a particular office who prepare tax returns for clients. Suppose that for a particular type of complex form, the number of errors made by the first preparer has a Poisson distribution with mean value \({{\rm{\mu }}_{\rm{1}}}\), the number of errors made by the second preparer has a Poisson distribution with mean value \({{\rm{\mu }}_{\rm{2}}}\), and that each CPA prepares the same number of forms of this type. Then if a form of this type is randomly selected, the function

\({\rm{p(x;}}{{\rm{\mu }}_{\rm{1}}}{\rm{,}}{{\rm{\mu }}_{\rm{2}}}{\rm{) = }}{\rm{.5}}\frac{{{{\rm{e}}^{{\rm{ - }}{{\rm{\mu }}_{\rm{1}}}}}{\rm{\mu }}_{\rm{1}}^{\rm{x}}}}{{{\rm{x!}}}}{\rm{ + }}{\rm{.5}}\frac{{{{\rm{e}}^{{\rm{ - }}{{\rm{\mu }}_{\rm{2}}}}}{\rm{\mu }}_{\rm{2}}^{\rm{x}}}}{{{\rm{x!}}}}{\rm{ x = 0,1,2,}}...\)

gives the \({\rm{pmf}}\) of \({\rm{X = }}\)the number of errors on the selected form.

a. Verify that \({\rm{p(x;}}{{\rm{\mu }}_{\rm{1}}}{\rm{,}}{{\rm{\mu }}_{\rm{2}}}{\rm{)}}\) is in fact a legitimate \({\rm{pmf}}\) (\( \ge {\rm{0}}\) and sums to \({\rm{1}}\)).

b. What is the expected number of errors on the selected form?

c. What is the variance of the number of errors on the selected form?

d. How does the \({\rm{pmf}}\) change if the first CPA prepares \({\rm{60\% }}\) of all such forms and the second prepares \({\rm{40\% }}\)?

A company that produces fine crystal knows from experience that 10% of its goblets have cosmetic flaws and must be classified as "seconds."

a. Among six randomly selected goblets, how likely is it that only one is a second?

b. Among six randomly selected goblets, what is the probability that at least two are seconds?

c. If goblets are examined one by one, what is the probability that at most five must be selected to find four that are not seconds?

Consider writing onto a computer disk and then sending it through a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with parameter\({\rm{\mu = }}{\rm{.2}}\). (Suggested in 鈥淎verage Sample Number for Semi-Curtailed Sampling Using the Poisson Distribution,鈥� J. Quality Technology,\({\rm{1983 = 126 - 129}}\).) a. What is the probability that a disk has exactly one missing pulse? b. What is the probability that a disk has at least two missing pulses? c. If twodisks are independently selected, what is the probability that neither contains a missing pulse?

A library subscribes to two different weekly news magazines, each of which is supposed to arrive in Wednesday鈥檚 mail. In actuality, each one may arrive on Wednesday, Thursday, Friday, or Saturday. Suppose the two arrive independently of one another, and for each one\(P\left( {Wed.} \right) = 0.3\), \(P\left( {Thurs.} \right) = 0.4\), \(P\left( {Fri.} \right) = 0.2\), and\(P\left( {Sat.} \right) = 0.1\). Let Y = the number of days beyond Wednesday that it takes for both magazines to arrive (so possible Y values are 0, 1, 2, or 3). Compute the pmf of Y. (Hint: There are 16 possible outcomes; \(Y\left( {W,W} \right) = {\bf{0}}\),\(Y\left( {F,Th} \right) = 2\), and so on.)

A family decides to have children until it has three children of the same gender. Assuming P(B) = P(G) =\({\rm{.5}}\), what is the pmf of X = the number of children in the family?
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