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Chapter 1: 1.1 (page 12)

For each of the following hypothetical populations, give

a plausible sample of size 4:

a. All distances that might result when you throw a football

b. Page lengths of books published 5 years from now

c. All possible earthquake-strength measurements (Richter scale) that might be recorded in California during the next year

d. All possible yields (in grams) from a certain chemical reaction carried out in a laboratory.

Short Answer

Expert verified

a.\(\left\{ {50,45,40,35} \right\}\)

b.\(\left\{ {700,490,800,500} \right\}\)

c.\(\left\{ {5.2,{\rm{ }}6.5,{\rm{ }}5,{\rm{ }}7} \right\}\)

d. \(\left\{ {60{\rm{gm}},{\rm{ }}57{\rm{gm}},{\rm{ }}40{\rm{gm}},{\rm{ }}80{\rm{gm}}} \right\}\)

Step by step solution

01

Given information

Four populations are provided.

02

Provide one possible sample of size 4.

a.

Assuming that the distance is measured in feet.

The possible sample of size 4 for all distances that might result when a football is thrown is given as,

\(\left\{ {50,45,40,35} \right\}\)

b.

The possible sample of size 4 forpage lengths of books published 5 years from nowis given as,

\(\left\{ {700,490,800,500} \right\}\)

03

Provide one possible sample of size 4.

c.

The possible sample of size 4 forall possible earthquake-strength measurements (Richter scale) that might be recorded in California during the next yearis given as,

\(\left\{ {5.2,{\rm{ }}6.5,{\rm{ }}5,{\rm{ }}7} \right\}\)

d.

The possible sample of size 4 forall possible yields (in grams) from a certain chemical reaction carried out in a laboratoryis given as,

\(\left\{ {60{\rm{gm}},{\rm{ }}57{\rm{gm}},{\rm{ }}40{\rm{gm}},{\rm{ }}80{\rm{gm}}} \right\}\)

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Most popular questions from this chapter

Let \({\rm{X}}\) denote the amount of space occupied by an article placed in a \({\rm{1 - f}}{{\rm{t}}^{\rm{3}}}\) packing container. The pdf of \({\rm{X}}\) is

\({\rm{f(x) = }}\left\{ {\begin{array}{*{20}{c}}{{\rm{90}}{{\rm{x}}^{\rm{8}}}{\rm{(1 - x)}}}&{{\rm{0 < x < 1}}}\\{\rm{0}}&{{\rm{ otherwise }}}\end{array}} \right.\)

a. Graph the pdf. Then obtain the cdf of \({\rm{X}}\) and graph it. b. What is \({\rm{P(X}} \le {\rm{.5)}}\) (i.e., \({\rm{F(}}{\rm{.5)}}\))? c. Using the cdf from (a), what is \({\rm{P(}}{\rm{.25 < X}} \le {\rm{.5)}}\)? What is \({\rm{P(}}{\rm{.25}} \le {\rm{X}} \le {\rm{.5)}}\)? d. What is the \({\rm{75th}}\) percentile of the distribution? e. Compute \({\rm{E(X)}}\) and \({{\rm{\sigma }}_{\rm{X}}}\). f. What is the probability that \({\rm{X}}\) is more than \({\rm{1}}\) standard deviation from its mean value?

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Let \({\rm{X}}\) denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is

\({\rm{F(x) = }}\left\{ {\begin{array}{*{20}{l}}{\rm{0}}&{{\rm{x < 0}}}\\{\frac{{{{\rm{x}}^{\rm{2}}}}}{{\rm{4}}}}&{{\rm{0拢 x < 2}}}\\{\rm{1}}&{{\rm{2\拢 x}}}\end{array}} \right.\)

a. Calculate\({\rm{P(X拢 1)}}\).

b. Calculate\({\rm{P(}}{\rm{.5拢 X拢 1)}}\).

c. Calculate\({\rm{P(X > 1}}{\rm{.5)}}\).

d. What is the median checkout duration \({\rm{\tilde \mu }}\) ? (solve\({\rm{5 = F(\tilde \mu ))}}\).

e. Obtain the density function\({\rm{f(x)}}\).

f. Calculate\({\rm{E(X)}}\).

g. Calculate \({\rm{V(X)}}\)and\({{\rm{\sigma }}_{\rm{X}}}\).

h. If the borrower is charged an amount \({\rm{h(X) = }}{{\rm{X}}^{\rm{2}}}\) when checkout duration is\({\rm{X}}\), compute the expected charge\({\rm{E(h(X))}}\).

Blood pressure values are often reported to the nearest5 mmHg (100, 105, 110, etc.). Suppose the actual bloodpressure values for nine randomly selected individuals are

118.6 127.4 138.4 130.0 113.7 122.0 108.3131.5 133.2

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a. What is the probability that after \({\rm{2hr}}{\rm{. }}\)of flying, the second plane has not caught up to the first plane?

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