(a) Make a frequency distribution and histogram (using appropriate bins) for these $28$ observations on the amount spent for dinner for four in downtown Chicago on Friday night. (b) Repeat the exercise, using a different number of bins. Which is preferred? Why?

$$\begin{array}{rrrrrrr}95 & 103 & 109 & 170 & 114 & 113 & 107 \\ 124 & 105 & 80 & 104 & 84 & 176 & 115 \\ 69 & 95 & 134 & 108 & 61 & 160 & 128 \\ 68 & 95 & 61 & 150 & 52 & 87 & 136\end{array}$$

At an altitude of $10,000 \mathrm{~ft}$, the partial pressure of oxygen in the lungs is about $68 \mathrm{~mm} \mathrm{Hg}$. What is the concentration in $\mathrm{mg} / \mathrm{L}$ of dissolved $\mathrm{O}_2$ in blood (or water) at this partial pressure and a normal body temperature of $37^{\circ} \mathrm{C}$ ? The solubility of $\mathrm{O}_2$ in water at $37^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$ partial pressure is $1.93 \times 10^{-3} \mathrm{~mol} / \mathrm{L}$.

Use the following information. The table below shows the rebounding totals for the 2003 Los Angeles Sparks.

$$\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline 141 & 231 & 220 & 126 & 175 & 55 & 29 & 68 & 19 & 32 & 19 & 21 & 6 & 23 & 1 \\ \hline \end{array}$$

Which measure of central tendency best represents the data? Explain.

Thirty patients had their glucose levels tested. The results are given with each result having a unit of milligrams per 100 milliliters (mg/100 mL).
85 100 72 92 76 83 88 96 80 103 70 79 91 82 90
101 92 93 85 74 98 71 87 80 92 85 99 85 68 81
a. Find the mean.
b. Find the median.
c. Find the mode.

Scientists have decided that there may be a relationship between temperature and the number of chirps produced by crickets. The table gives the temperature and the number of chirps per minute for several cricket samples.

(a) Make a frequency distribution and histogram for the monthly off-campus rent paid by 30 students. (b) Repeat the exercise, using a different number of bins. Which is preferred? Why?

Consider the following hypothesis test:

$$\begin{array} { l } { H _ { 0 } : p \geq .75 } \\ { H _ { \mathrm { a } } : p < .75 } \end{array}$$

$$\begin{array} { l } { \text { A sample of } 300 \text { items was selected. Compute the } p \text { -value and state your conclusion for } } \\ { \text { each of the following sample results. Use } \alpha = .05 . } \\ { \text { a. } \overline { p } = .68 } & { \text { c. } \overline { p } = .70 } \\ { \text { b. } \overline { p } = .72 } & { \text { d. } \quad \overline { p } = .77 } \end{array}$$

The upper arm length of females over 20 years old in the United States is approximately Normal with mean 35.8 centimeters (cm) and standard deviation 2.1 cm. Use the 68-95-99.7 rule to answer the following questions. (Start by making a sketch like the given figure.)

(a) What range oflengt hs covers almost all (99.7%) of this distribution?

(b) What percent of women over 20 have upper arm lengths less than 33.7 cm?

The table shows the number of customers visiting a supermarket on various days. Estimate the mean number of customers per day.

$$\begin{matrix} \text{Number of customers} & \text{Frequency}\\\text{250-299} & \text{14}\\ \text{300-349} & \text{34}\\ \text{350-399} & \text{68}\\ \text{400-449} & \text{72}\\ \text{450-499} & \text{54}\\ \text{500-549} & \text{23}\\ \text{550-599} & \text{7}\\ \end{matrix}$$

Below displayed the ages (in years) of the Presidents at the time of their deaths.

$$\begin{array}{llllllll}67 & 90 & 83 & 85 & 73 & 80 & 78 & 79 \\ 68 & 71 & 53 & 65 & 74 & 64 & 77 & 56 \\ 66 & 63 & 70 & 49 & 57 & 71 & 67 & 71 \\ 58 & 60 & 72 & 67 & 57 & 60 & 90 & 63 \\ 88 & 78 & 46 & 64 & 81 & 93 & 93 & \end{array}$$

6. If it does not, provide a reason why.

The resting heart rates for a sample of individuals are normally distributed with a mean of $70$ and a standard deviation of $15$. Use the $68-95-99.7$ rule to find the percentage of heart rates in each of the following categories.

a. less than $55$ $\quad$ b. less than $40$ $\quad$ c. less than $85$

d. less than $100$ $\quad$ e. greater than $85$ $\quad$ f. greater than $55$

g. greater than $40$ $\quad$ h. between $55$ and $85$

(a) Show that, for an ideal gas, the speed of sound given by Equation $v=\sqrt{\frac{\gamma p}{\rho}}$ can be written $v_{\text {sound }}=\sqrt{\gamma k T / m}$.

(b) For diatomic gases like $\mathrm{N}_2$ and $\mathrm{O}_2$ that are the dominant constituents of air, $\gamma=7 / 5$. Use your result to show that, for diatomic gases, the speed of sound is about $68 \%$ of the thermal speed given by Equation $v_{\mathrm{th}}=\sqrt{\frac{3 k T}{m}}$.

The numbers of various multiple births in the United States for the past 10 years are listed. Determine the range, variance, and standard deviation of the data sets. Which set of data is the most variable?

Scientists have decided that there may be a relationship between temperature and the number of chirps produced by crickets. The table gives the temperature and the number of chirps per minute for several cricket samples.