Chapter 17

Find the mean of the data set. $$ 2,4,6,8 $$

Find the mean and standard deviation of the data set. $$ 13,14,19,28,30,31,50 $$

Give the probability, as a percentage, of picking the indicated card from a deck. King of Hearts

Find the mean of the data set. $$ 2,4,6,8,100 $$

Find the mean and standard deviation of the data set. $$ 25,30,32,32,41,45,57,62 $$

Give the probability, as a percentage, of picking the indicated card from a deck. Red card

Find the mean of the data set. $$ 102,104,106,108 $$

Find the mean and standard deviation of the data set. $$ 81,57,14,98,20,20,6 $$

Give the probability, as a percentage, of picking the indicated card from a deck. Face card

Find the mean of the data set. $$ -5,-2,0,5,2 $$

Find the mean and standard deviation of the data set. $$ 16,66,30,99,74,50,35,7 $$

Give the probability, as a percentage, of picking the indicated card from a deck. 2 or 3

Find the mean and standard deviation of the data set. $$ 12,-8,13,-15,60,-72,23,-13 $$

Find the mean of the data set. $$ 5,2,19,6,5,2 $$

Give the probability, as a percentage, of picking the indicated card from a deck. Spade

Find the mean and standard deviation for each of the following data sets. (a) 1,2,3,4,5,6,7 (b) 4,4,4,4,4,4,4 (c) 2,2,4,4,4,6,6

Find the mean of the data set. $$ 5,5,5,0,0,0,0,0,5,5 $$

Find \(\bar{a}\). $$ a_{i}=i^{2}, i=1, \ldots, 6 $$

The clutch size of a bird is the number of eggs laid by the bird. Table 17.7 shows the clutch size of six different birds labeled (i)-(vi). What is the (a) Mean clutch size? (b) Standard deviation of these clutch sizes? $$ \begin{array}{c|c|c|c|c|c|c} \hline \text { Bird } & \text { (i) } & \text { (ii) } & \text { (iii) } & \text { (iv) } & \text { (v) } & \text { (vi) } \\ \hline \text { Clutch size } & 6 & 7 & 2 & 3 & 7 & 5 \\ \hline \end{array} $$

The sale prices (in \(\$ 1000\) s) for eight houses on a certain road are: \(\$ 820, \$ 930, \$ 780, \$ 950, \$ 3540, \$ 680, \$ 920,\) \(\$ 900 .\) Find the mean and standard deviation of the (a) Eight houses. (b) Seven similar houses (leave out the top-priced house).

Find \(\bar{a}\). $$ a_{i}=2 i, i=1, \ldots, 10 $$

If your music player has four playlists, Rock (233 songs), Hip-Hop (157 songs), Jazz (107 songs) and Latin ( 258 songs), and you select the shuffle mode, what is the probability, given as a percentage, of starting with a song from (a) Rock (b) Hip-Hop (c) Jazz (d) Latin.

A naturalist collects samples of a species of lizard and measures their lengths. Give the (a) sample size (b) mean (c) range (d) \(\quad\) standard deviation. $$ \begin{array}{l|c|c|c|c|c} \hline \text { Lizard no. } & 1 & 2 & 3 & 4 & 5 \\ \hline \text { Length }(\mathrm{cm}) & 5.8 & 6.8 & 6.9 & 6.9 & 7.0 \\ \hline \text { Lizard no. } & 6 & 7 & 8 & 9 & 10 \\ \hline \text { Length }(\mathrm{cm}) & 7.1 & 7.1 & 7.1 & 7.2 & 8.1 \\ \hline \end{array} $$

Find \(\bar{a}\). $$ a_{i}=2, i=1, \ldots, 10 $$

The probability expressions refer to drawing a card from a standard deck of cards. State in words the meaning of the expression and give the probability as a fraction. $$ P(\text { Red }) $$

A naturalist collects samples of a species of lizard and measures their lengths. Give the (a) sample size (b) mean (c) range (d) \(\quad\) standard deviation. $$ \begin{array}{l|c|c|c|c|c} \hline \text { Lizard no. } & 1 & 2 & 3 & 4 & 5 \\ \hline \text { Length }(\mathrm{cm}) & 5.8 & 5.9 & 5.9 & 6.0 & 6.5 \\ \hline \text { Lizard no. } & 6 & 7 & 8 & 9 & 10 \\ \hline \text { Length }(\mathrm{cm}) & 7.9 & 7.9 & 8.0 & 8.0 & 8.1 \\ \hline \end{array} $$

Find \(\bar{a}\). $$ a_{i}=2^{i}, i=1, \ldots, 5 $$

A naturalist collects samples of a species of lizard and measures their lengths. Give the (a) sample size (b) mean (c) range (d) \(\quad\) standard deviation. $$ \begin{array}{c|c|c|c|c|c|c|c} \hline \text { Length }(\mathrm{cm}) & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \text { No. lizards } & 1 & 6 & 26 & 36 & 23 & 6 & 2 \\ \hline \end{array} $$

Find \(\bar{a}\). $$ a_{i}=i / 2 \text { and } i=1, \ldots, 5 $$

The probability expressions refer to drawing a card from a standard deck of cards. State in words the meaning of the expression and give the probability as a fraction. $$ P(\operatorname{Red} \cap \text { King }) $$

The probability expressions refer to drawing a card from a standard deck of cards. State in words the meaning of the expression and give the probability as a fraction. \(P(\) King \(\cap\) Red \()\)

Table 17.2 shows the number of passengers taking a particular daily flight from Boston to Washington over the course of a week. Find the mean number of passengers for the week. $$ \begin{array}{c|c|c|c|c|c|c|c} \hline \text { Day } & \text { Mon } & \text { Tue } & \text { Wed } & \text { Thur } & \text { Fri } & \text { Sat } & \text { Sun } \\ \hline \text { Passengers } & 228 & 110 & 215 & 178 & 140 & 72 & 44 \\ \hline \end{array} $$

The probability expressions refer to drawing a card from a standard deck of cards. State in words the meaning of the expression and give the probability as a fraction. \(P(\) King \(\mid\) Red \()\)

Suppose you record the hours of daylight in Tucson, Arizona, each day for a year and find the mean amount. (a) What do you expect for an approximate mean? (b) How would your data compare with a student doing the same project in Anchorage, Alaska? (c) How would your standard deviation compare with a student doing the same project in Anchorage, Alaska?

Find the standard deviation of the data set. $$ 20,30,40,80,130 $$

Catherine has the following phone bills over a twelvemonth period: \(\$ 32, \$ 27, \$ 20, \$ 40, \$ 33, \$ 20, \$ 32, \$ 30,\) \(\$ 36, \$ 31, \$ 37, \$ 22\) (a) What is the average phone bill? (b) Suppose Catherine spends \(\$ 5\) more on phone bills each month. What happens to her average phone bill? What if she spends \(\$ 10\) more each month? (c) Suppose she spends \(\$ 60\) more on the highest phone bill, but the same amount on the other 11 bills. What happens to her average phone bill? What if she spends \(\$ 120\) more on the highest bill?

The probability expressions refer to drawing a card from a standard deck of cards. State in words the meaning of the expression and give the probability as a fraction. \(P(\) Red \(\mid\) King \()\)

The probability expressions refer to drawing a card from a standard deck of cards. State in words the meaning of the expression and give the probability as a fraction. \(P\) (Heart \(\mid\) Red)

The probability expressions refer to drawing a card from a standard deck of cards. State in words the meaning of the expression and give the probability as a fraction. \(P(\) Red \(\mid\) Heart \()\)

On the back cover of the classic jazz album Kind of Blue by Miles Davis, the lengths of the five songs are shown in parentheses: \((9: 02),(9: 33),(5: 26),(11: 31),\) (9:25). What is the mean length of a song on this album?

Find the standard deviation of the data set. Five readings each equaling 120 , three readings each equaling 130 , two readings each equaling 140 , four readings each equaling 150 , and 1 reading equaling \(160 .\)

Find the mean of \(1,2,3, \ldots, n,\) if \(n\) is (a) 3 (b) 4 (c) 5 (d) 6 (e) \(2 \mathrm{k}\) (f) \(2 \mathrm{k}+1\)

A sample of \(n\) frogs has a total weight of \(W\) grams. (a) What is the mean weight of a frog in the sample? (b) The largest frog eats the smallest one. What is the mean weight now?

Table 17.18 shows the number of flights carrying a given number of passengers over a ten-week time period. $$\begin{array}{c|c|c|c|c} \hline \text { Passengers } & 0-50 & 51-100 & 101-150 & 151-200 \\ \hline \text { Flights } & 3 & 10 & 16 & 20 \\ \hline \text { Passengers } & 201-250 & 251-300 & 301-350 & \\ \hline \text { Flights } & 15 & 4 & 2 & \\ \hline \end{array}$$ (a) What is the probability, given as a percentage, that a flight picked at random from this group of flights carried more than 200 passengers? (b) What is the probability that a passenger picked at random from among this group of passengers was on a plane carrying more than 200 passengers?

Table 17.19 gives the vehicle occupancy for people driving to work in 1990 as determined by the US Census. For instance, 84,215,000 people drove alone and 12,078,000 people drove in 2 -person car pools. Picking at random, what is the probability, given as a percentage, that: (a) A commuter drives to work alone? (b) A vehicle carries 4 or more people?$$ \begin{array}{c|c|c|c|c|c|c|c} \hline \text { Occupancy } & 1 & 2 & 3 & 4 & 5 & 6 & 7+ \\ \hline \text { People, } 1000 \mathrm{~s} & 84,215 & 12,078 & 2,001 & 702 & 209 & 97 & 290 \\ \hline \end{array} $$

A sample of 20 frogs has a total weight of \(W\) grams. (a) What is the mean weight (in grams per frog) of the sample? (b) One of the frogs has been mis-weighed. Instead of \(x\) grams, its weight is \(y\) grams. What is the corrected mean weight of the sample?

There are 54 M\&Ms in a packet: 14 blue, 4 brown, 6 green, 14 orange, 7 red, and 9 yellow. (a) For each color, find the probability, as a percentage, of randomly picking that color from the packet. (b) Find the probability, as a percentage, of randomly picking a blue if someone has eaten all the reds.

A sample of \(n_{1}\) frogs has a total weight of \(W_{1}\) grams. A second sample of \(n_{2}\) frogs has a total weight of \(W_{2}\) grams. (a) What is the mean weight (in grams per frog) of each sample? (b) What is the mean weight of all the frogs in both samples? Does it equal the average of the mean weights of the samples taken separately?

Consider the following list of sale prices (in \(\$ 1000 \mathrm{~s}\) ) for eight houses on a certain road: \(\$ 820, \$ 930, \$ 780,\) \(\$ 950, \$ 3540, \$ 680, \$ 920, \$ 900 .\) One of the houses is worth much more than the other seven because it is much larger, it is set well back from the road, and it is adjacent to the shore of a lake to which it has private access. (a) What is the mean price of these eight houses? (b) Is the mean a good description of the value of the houses on this block? Explain your reasoning.

The classic album Kind of Blue by Miles Davis lists five songs with their lengths in parentheses. If your music player is currently playing this album in shuffle mode, what is the probability, given as a percentage, that when you plug in your earphones you hear: (a) So What \((9: 02)\) (b) Freddie Freeloader \((9: 33)\) (c) Blue in Green (5:26) (d) All Blue (11:31) (e) Flamenco Sketches \((9: 25)\).