Listed below are annual salaries (in thousands of dollars) for a simple random sample of NCAA Division 1-A head football coaches (based on data from the New York Times).

$$\begin{array}{llllllllll} 235 & 159 & 492 & 530 & 138 & 125 & 128 & 900 & 360 & 212 \end{array}$$

d. Find the variance $s^2$ and express the result in appropriate units.

A random sample of 5 bank presidents indicated annual salaries of $395,000,$521,000, $483,000,$479,000, and $510,000. Find the variance of this set.

A simple random sample of 40 salaries of NCAA football coaches has a mean of 415,953 dollars. Suppose that $\sigma=\$ 463,364$.

b. Construct a 95% confidence interval estimate of the mean salary of an NCAA football coach.

Monthly Sales Data. A simple random sample of 5 months of sales data provided the following information:

$$\begin{array}{lrrrrr}\text { Month: } & 1 & 2 & 3 & 4 & 5 \\ \text { Units Sold: } & 94 & 100 & 85 & 94 & 92\end{array}$$

a. Develop a point estimate of the population mean number of units sold per month.

The salaries of the ten employees at the XYZ Corporation are listed below.

$$\begin{array}{l} \$ 54,000, \$ 75,000, \$ 55,000, \$ 62,000, \$ 226,000, \\ \$ 65,000, \$ 59,000, \$ 61,000, \$ 162,000, \$ 59,000 \end{array}$$

Find the median of the salaries.

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. Then answer the given questions.

Listed below are the annual salaries for a simple random sample of NCAA football coaches (based on data from USA Today). How do the mean and median change if the highest salary is omitted?

$150,000$300,000

$350,147$232,425

$360,000$1,231,421

$810,000$229,000

A simple random sample of pages from Merriam-Webster's Collegiate Dictionary. 11th edition was obtained. Listed below are the numbers of defined words on those pages, and they are arranged in order. Make a boxplot and include the values of the 5 -number summary.

$$\begin{array}{llllllllll} 34 & 36 & 39 & 43 & 51 & 53 & 62 & 63 & 73 & 79 \end{array}$$

Compare your answers in the previous exercise. How much influence does the sampling method have on your chances of winning a prize?

A circular coil of 16 turns and radius $10 \mathrm{~cm}$ carrying a current of $0.75$ A rests with its plane normal to an external field of magnitude 5.0 10 T. The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly an d released, it oscillates about its stable equilibrium with a frequency of $2.0 \mathrm{~s}$. What is the moment of inertia of the coil about its axis of rotation?

Given a simple random sample of 20 speeds of cars on Highway 405 in California, you want to test the claim that the sample values are from a population with a mean greater than the posted speed limit of $65 \mathrm{mi} / \mathrm{h}$. Is it necessary to determine whether the sample is from a normally distributed population? If so, what methods can be used to make that determination?

Given the following observations in a simple random sample from a population that is approximately normally distributed, construct and interpret the $95 \%$ and $99 \%$ confidence intervals for the mean:

$$\begin{array}{llllllllll}66 & 34 & 59 & 56 & 51 & 45 & 38 & 58 & 52 & 52 \\ 50 & 34 & 42 & 61 & 53 & 48 & 57 & 47 & 50 & 54\end{array}$$

A coach must select two players to serve as captains. He wants to randomly select two players to be the captains. Obtain a simple random sample of size 2 from the following list: Mady, Breanne, Evin, Tori, Emily, Clair, Caty, Jory, Payton, Jordyn. Write a short description of the process you used to generate your sample.

Listed below are annual salaries (in thousands of dollars) for a simple random sample of NCAA Division 1-A head football coaches (based on data from the New York Times).

$$\begin{array}{llllllllll} 235 & 159 & 492 & 530 & 138 & 125 & 128 & 900 & 360 & 212 \end{array}$$

c. Find the standard deviation $s$ and express the result in dollars instead of thousands of dollars.

Determine whether the zero state is a stable equilibrium of the dynamical system $\vec{x}(t+1)=A \vec{x}(t).$

$$A=\left[\begin{array}{lll} 0.3 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.3 \end{array}\right]$$