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Chapter 6: Q. 66 (page 382)
The standard deviation of is
(a)
(b)
(c)
(d)
(e)
The standard deviation of is option
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45. Too cool at the cabin? During the winter months, the temperatures at the Stameses' Colorado cabin can stay well below freezing or for weeks at a time. To prevent the pipes from freezing, Mrs. Stames sets the thermostat at . She also buys a digital thermometer that records the indoor temperature each night at midnight. Unfortunately, the thermometer is programmed to measure the temperature in degrees Celsius. Based on several years' worth of data, the temperature in the cabin at midnight on a randomly selected night follows a Normal distribution with mean and standard deviation.
(a) Let the temperature in the cabin at midnight on a randomly selected night in degrees Fahrenheit (recall that . Find the mean and standard deviation of .
(b) Find the probability that the midnight temperature in the cabin is below . Show your work.
How well does it 铿乼? () Discuss what s, , and the residual plot tells you about this linear regression model.
In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?
(a)
(b)
(c)
(d)
(e)
Most states and Canadian provinces have government-sponsored lotteries. Here is a simple lottery wager, from the Tri-State Pick game that New Hampshire shares with Maine and Vermont. You choose a number with digits from to ; the state chooses a three-digit winning number at random and pays you if your number is chosen. Because there are numbers with three digits, you have a probability of of winning. Taking to be the amount your ticket pays you, the probability distribution of is
(a) Show that the mean and standard deviation of are and .
(b) If you buy a Pick 3 ticket, your winnings are , because it costs to play. Find the mean and standard deviation of . Interpret each of these values in context.
Ana is a dedicated Skee Ballplayer (see photo) who always rolls for the -point slot. The probability distribution of Ana's score on a single roll of the ball is shown below. You can check that and .
(a) A player receives one ticket from the game for every points scored. Make a graph of the probability distribution for the random variable number of tickets Ana gets on a randomly selected throw. Describe its shape.
(b) Find and interpret .
(c) Compute and interpret .
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