Chapter 21

Find the correlation coefficient for each set of data. $$\begin{array}{rr} \hline-8.00 & -6.238 \\ -6.66 & -3.709 \\ -5.33 & -0.712 \\ -4.00 & 1.887 \\ -2.66 & 4.628 \\ -1.33 & 7.416 \\ 0.00 & 10.20 \\ 1.33 & 12.93 \\ 2.66 & 15.70 \\ 4.00 & 18.47 \\ 5.33 & 21.32 \\ 6.66 & 23.94 \\ 8.00 & 26.70 \\ 9.33 & 29.61 \\ 10.60 & 32.35 \\ 12.00 & 35.22 \\ \hline \end{array}$$

The heights of 49 randomly chosen students at Tech College were measured. Their mean \(\bar{x}\) was found to be 69.47 in., and their standard deviation \(s\) was 2.35 in. Estimate the mean \(\mu\) of the entire population of students at Tech College with a confidence level of \(68 \%\).

We draw a ball from a bag that contains 8 green balls and 7 blue balls. What is the probability that a ball drawn at random will be green?

Find the mean of the following set of grades: $$85 \quad 74 \quad 69 \quad 59 \quad 60 \quad 96 \quad 84 \quad 48 \quad 89 \quad 76 \quad 96 \quad 68 \quad 98 \quad 79 \quad 76$$

Find the correlation coefficient for each set of data. $$\begin{array}{lr} \hline-20.0 & 82.29 \\ -18.5 & 73.15 \\ -17.0 & 68.11 \\ -15.6 & 59.31 \\ -14.1 & 53.65 \\ -12.6 & 45.90 \\ -11.2 & 38.69 \\ -9.73 & 32.62 \\ -8.26 & 24.69 \\ -6.80 & 18.03 \\ -5.33 & 11.31 \\ -3.86 & 3.981 \\ -2.40 & -2.968 \\ -0.93 & -9.986 \\ 0.53 & -16.92 \\ 2.00 & -23.86 \\ \hline \end{array}$$

A card is drawn from a deck containing 13 hearts, 13 diamonds, 13 clubs, and 13 spades. What is the chance that a card drawn at random will be a heart?

Find the mean of the following set of weights: $$\begin{array}{llllllll} 173 & 127 & 142 & 164 & 163 & 153 & 116 & 199 \end{array}$$

Find the correlation coefficient for each set of data. $$\begin{array}{rr} \hline-11.0 & -65.30 \\ -9.33 & -56.78 \\ -7.66 & -47.26 \\ -6.00 & -37.21 \\ -4.33 & -27.90 \\ -2.66 & -18.39 \\ -1.00 & -9.277 \\ 0.66 & 0.081 \\ 2.33 & 9.404 \\ 4.00 & 18.93 \\ 5.66 & 27.86 \\ 7.33 & 37.78 \\ 9.00 & 46.64 \\ 10.6 & 56.69 \\ 12.3 & 64.74 \\ 14.0 & 75.84 \\ \hline \end{array}$$

If we toss four coins, what is the probability of getting two heads and two tails? [Hint: This experiment has 16 possible outcomes (HHHH, HHHT, TTTT).]

If we toss four coins, what is the probability of getting one head and three tails?

If we throw two dice, what is the probability that their sum is \(9 ?\) [Hint: List all possible outcomes, \((1,1),(1,2),\) and so on, and count those that have a sum of 9.1

If two dice are thrown, what is the probability that their sum is \(7 ?\)

A student's grades and the weight of each grade are given in the following table. Find their weighted mean. $$\begin{array}{l|rr} \hline & \text { Grade } & \text { Weight } \\ \hline \text { Hour exam } & 83 & 5 \\ \text { Hour exam } & 74 & 5 \\ \text { Quiz } & 93 & 1 \\ \text { Final exam } & 79 & 10 \\\ \text { Report } & 88 & 7 \\ \hline \end{array}$$

A die is rolled twice. What is the probability that both rolls will give a six?

A student receives hour-test grades of \(86,92,68,\) and \(75,\) a final exam grade of \(82,\) and a project grade of \(88 .\) Find the weighted mean if each hour-test counts for \(15 \%\) of his grade, the final exam counts for \(30 \%,\) and the project counts for \(10 \%.\)

The following table shows the population of a certain town for the years \(1920-1930:\) $$\begin{array}{lc} \hline \text { Year } & \text { Population } \\ \hline 1920 & 5364 \\ 1921 & 5739 \\ 1922 & 6254 \\ 1923 & 7958 \\ 1924 & 7193 \\ 1925 & 6837 \\ 1926 & 7245 \\ 1927 & 7734 \\ 1928 & 8148 \\ 1929 & 8545 \\ 1930 & 8623 \\ \hline \end{array}$$ Make a scatter plot and an \(x-y\) graph of the population versus the year.

We draw four cards from a deck, replacing each before the next is drawn. What chance is there that all four draws will be a red card?

At a certain school, \(55 \%\) of the students have brown hair, \(15 \%\) have blue eyes, and \(7 \%\) have both brown hair and blue eyes. What is the probability that a student chosen at random will have either brown hair or blue eyes, or both brown hair and blue eyes?

Find the \(68 \%\) confidence interval for drawing a heart from a deck of cards for 200 draws from the deck, replacing the card each time before the next draw.

Find the probability that a card drawn from a deck will be either a "picture" card (jack, queen, or king) or a spade card.

On a certain production line, \(5 \%\) of the parts are underweight and \(8 \%\) are overweight. What is the probability that one part selected at random is either underweight or overweight?

A binomial experiment is repeated \(n\) times, with a probability \(p\) of success on one trial. Find the probability \(P(x)\) of \(x\) successes, if $$n=5, p=0.4, \text { and } x=3.$$

A binomial experiment is repeated \(n\) times, with a probability \(p\) of success on one trial. Find the probability \(P(x)\) of \(x\) successes, if $$n=7, p=0.8, \text { and } x=4$$

A binomial experiment is repeated \(n\) times, with a probability \(p\) of success on one trial. Find the probability \(P(x)\) of \(x\) successes, if $$n=7, p=0.8, \text { and } x=6$$

A binomial experiment is repeated \(n\) times, with a probability \(p\) of success on one trial. Find the probability \(P(x)\) of \(x\) successes, if $$n=9, p=0.3, \text { and } x=6$$

What is the probability of tossing 7 heads in 10 tosses of a fair coin?

If male and female births are equally likely, what is the probability of five births being all girls?

A certain multiple-choice test has 20 questions, each of which has four choices, only one of which is correct. If a student were to guess every answer, what is the probability of getting 10 correct?

Find the quartiles and give the quartile range of the following data: $$28 \quad 39 \quad 46 \quad 53 \quad 69 \quad 71 \quad 83 \quad 94 \quad 102 \quad 117 \quad 126$$

Find the quartiles and give the quartile range of the following data: \(1.33 \quad 2.28 \quad 3.59 \quad 4.96 \quad 5.23 \quad 6.89\) \(7.91 \quad 8.13 \quad 9.44 \quad 10.6 \quad 11.2 \quad 12.3\)