In 1957, an adaptation of "The Life You Save May Be Your Own" was broadcast on television. In the TV version, the ending was changed, according to O'Connor, "by having Shiftlet suddenly get a conscience and come back for the girl." Write a letter to the network that presented the show, either protesting or supporting this change. Give reasons for your opinion.

A TV remote control has keys for channels 0 through 9. IF you select one key at random. (a) What is the probability that you press a key for channel 6? (b) What is the probability that you press a key for an even number? (c) What is the probability that you press a key for a number less then 7?

Life Expectancy of Plasma TVs The life expectancy (in years) of a certain brand of plasma TV is a continuous random variable with probability density function

$$f(t)=9\left(9+t^2\right)^{-3 / 2} \quad(0 \leq t<\infty)$$

How long is one of these plasma TVs expected to last?

Which of the following situations would involve data that are best displayed In a box plot? (A) the number of each type of drink a cafeteria sells, (B) the response the most people gave to a survey on number of pets, (C) the number of points Liam scored in each basketball game this season, (D) the median age of a TV show's viewers

Consider a room that is initially at the outdoor temperature of $20^{\circ} \mathrm{C}$. The room contains a $100-\mathrm{W}$ lightbulb, a $110-\mathrm{W}$ TV set, a 200-W refrigerator, and a $1000-\mathrm{W}$ iron. Considering no heat transfer via the walls, find the rate of increase of the energy content of the room when all of these electric devices are on.

Use the following list of items to work the problem:

• New Year’s Eve celebrations in Times Square, New York
• A city’s sewer system
• New York subway system
• A skateboard
• Cable TV
• Niagara Falls

For each public good in the list, is there a free-rider problem? If not, how is the free-rider problem avoided?

Determine whether the study is an experiment or an observational study, and then identify a major problem with the study. In a survey conducted by USA Today, I 465 Internet users chose to respond to this question posted on the USA Today electronic edition: "ls news online as satisfying as print and TV news?" 52% of the respondents said "yes."

Calculate the de Broglie wavelength of an electron in your TV picture tube if it is accelerated by $20,000 ~\mathrm{V}$. Is it relativistic? How does its wave length compare to the size of the "neck" of the tube, typically $5$ cm? Do we have to worry about diffraction problems blurring our picture on the screen?

Weekly sales of an old brand of TV are given by $S(t)=100 e^{-t / 5}$ per week, where t is the number of weeks after the introduction of a competing brand. Estimate S(5) and $\left.\frac{d S}{d t}\right|_{t=5}$ and interpret your answers.

A psychologist named Dr. Richmond is researching how college students watch daytime TV. She estimates that during the afternoon, 45% of college students watch soap operas. She chooses a sample of 10 for further investigation. Using this, develop a probability distribution for the number of students in the sample who watch soap operas.

When placed outside and exposed to the atmosphere, an ice cube melts, forming a thin film of liquid on the ground. Overnight, the liquid freezes, returning to the initial temperature of the ice cube. The water making up the cube undergoes (a) a thermodynamic cycle, (b) a reversible process, (c) an irreversible process, (d) none of the above.

In this exercise, solve the given problems. All data are accurate to two significant digits unless greater accuracy is given.

A sponsor pays a total of $\$ 9500$ to run a commercial on two different TV stations. One station charges $\$ 1100$ more than the other. What does each charge to run the commercial?

In a TV game show, a contestant is given five cards with a different digit on each and is asked to arrange them to match the price of a brand-new car. If she gets the price right, she wins the car. What is the probability that she wins, assuming that she knows the first digit but must guess the remaining four?

The manufacturer of a metal stand for home TV sets must be sure that its product will not fail under the weight of the TV. Since some larger sets weigh nearly 300 pounds, the company's safety inspectors have set a standard of ensuring that the stands can support an average of over 500 pounds. Their inspectors regularly subject a random sample of the stands to increasing weight until they fail. They test the hypothesis

$$\mathrm { H } _ { 0 } : \mu = 500$$

against

$$\mathrm { H } _ { \mathrm { A } } : \mu > 500$$

, using the level of significance

$$\alpha = 0.01$$

. If the sample of stands fails to pass this safety test, the inspectors will not certify the product for sale to the general public. Explain what will happen if the inspectors commit a Type I error.