Based on past experience, $20 \%$ of the contacts made by a firm's sales representatives result in a sale being made. Charlie has contacted 100 potential customers but has made only 10 sales. Assume that Charlie's contacts represent a simple random sample of those who could have been called upon. Given this information:

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

Work in a group of four to plan your ten-year class reunion in Punta Cana, Dominican Republic. Plan how long the reunion will be, what activities people can participate in, and what food will be served. Create an invitation and present it to the class. After looking at all of the invitations, vote for the plan that you want to use for your class reunion.

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:

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

Test the given claim. Assume that both samples are independent simple random samples from populations having normal distributions.

A random sample of 13 four-cylinder cars is obtained, and the braking distances are measured and found to have a mean of $137.5 \mathrm{ft}$ and a standard deviation of $5.8 \mathrm{ft}$. A random sample of 12 six-cylinder cars is obtained and the braking distances have a mean of $136.3 \mathrm{ft}$ and a standard deviation of $9.7 \mathrm{ft}$. Use a $0.05$ significance level to test the claim that braking distances of four-cylinder cars and braking distances of six-cylinder cars have the same standard deviation.

Suppose you plan to take a random sample of 1,000 Hispanics in the United States. Assume that the distribution of origin has not changed since 2010.

a. What proportion of Hispanics in the United States in 2010 were of Mexican origin? What is the expected number of Hispanics in your sample who will be of Mexican origin?

b. What proportion of Hispanics in the United States in 2010 were of Puerto Rican origin? What is the expected number of Hispanics in your sample who will be of Puerto Rican origin?

c. Now suppose that you take a random sample of 1,000 Hispanics from your state and find 521 Hispanics of Mexican origin. A friend takes a second random sample of 1,500 Hispanics from your state and finds 847 of Mexican origin. What is the best estimate of the proportion of Hispanics in your state who are of Mexican origin?

d. Suppose you plan to take yet another random sample from your state, this time of 500 Hispanics. Based on your work in Part c, what is the best estimate of the expected number of Hispanics of Mexican origin you will find in this sample?

The number of dirt specks on a randomly selected square yard of polyethylene film of a certain type has a Poisson distribution with a mean value of 2 specks per square yard. Consider a random sample of $n=5$ film specimens, each having area 1 square yard, and let $\bar{X}$ be the resulting sample mean number of dirt specks. Obtain the first 21 probabilities in the $\bar{X}$ sampling distribution.

You must choose an SRS of 10 of the 440 retail outlets in New York that sell your company's products. How would you label this population to select a simple random sample?

(a) 001, 002, 003, . . . , 439, 440

(b) 000, 001, 002, . . . , 439, 440

(c) 1, 2, . . . ,439, 440

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

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

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.

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

A simple random sample of FICO credit rating scores was obtained, and the sorted scores are listed below. Make a boxplot and include the values of the 5-number summary.

$$\begin{array}{llllllllllll} 664 & 693 & 698 & 714 & 751 & 753 & 779 & 789 & 802 & 818 & 834 & 836 \end{array}$$

An ecologist wishes to mark off a circular sampling region having a radius $10{m}$. However, the radius of the resulting region is actually a random variable $R$ with pdf

$$f(r)=\left\{\begin{array}{cl} \frac{3}{4}\left[1-(10-r)^2\right] & 9 \leq r \leq 11 \\ 0 & \text { otherwise } \end{array}\right.$$

What is the expected area of the resulting circular region?

Quieres participar en un concurso literario para escritores jóvenes. Para la primera etapa del concurso, hay que entregar un plan del cuento. Usando el plan en la página 119 como modelo, prepara un plan para tu propio cuento. ¿Qué información vas a incluir alli y cómo piensas organizar el plan?