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:

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

Use the positive definite function $V(x, y)=x^{2}+y^{2}$ to argue that the system have asymptotically stable equilibrium points at the origin.

$$\begin{array}{l} x^{\prime}=-x-2 y^{2} \\ y^{\prime}=2 x y-y^{3} \end{array}$$

Why do you think many people considered Columbus' plan to be controversial?

The sampling distribution for the goodness of fit test is the

A. Poisson distribution
B. t distribution
C. normal distribution
D. chi-square distribution

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?

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

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

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.

Consider the system

$$\frac{d \vec{x}}{d t}=\left[\begin{array}{rr} -1 & k \\ k & -1 \end{array}\right] \vec{x},$$

where k is an arbitrary constant. For which values of k is the zero state a stable equilibrium solution?

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

Plan an investigation to determine the percentage by mass of cashews and almonds in a jar of mixed nuts.

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.

Listed below are sorted amounts of strontium90 (in millibecquerels or mBq ) in a simple random sample of baby teeth obtained from Pennsylvania residents born after 1979. Construct a boxplot and include the values of the 5-number summary.

$$128\ 130\ 133\ 137\ 138\ 142\ 142\ 144\ 147\ 149\ 151\ 151\ 151\ 155\ 156\ 161\ 163\ 163\ 166\ 172$$

Identify National Guard, attorney general, secretary of state, Missouri Plan.