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Chapter 6: Q.70 (page 403)
Explain whether the given random variable has a binomial distribution
Long or short? Put the names of all the students in your class in a hat. Mix them up, and draw four names without looking. Let the number whose last names have more than six letters.
The given distribution is not binomial
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Ms. Hall gave her class a -question multiple-choice quiz. Let the number of questions that a randomly selected student in the class answered correctly. The computer output below gives information about the probability distribution of X. To determine each student鈥檚 grade on the quiz (out of localid="1649489099543" ), Ms. Hall will multiply his or her number of correct answers by 10. Let localid="1649489106434" the grade of a randomly chosen student in the class.
localid="1649489113566"
(a) Find the mean of localid="1649489121120" . Show your method.
(b) Find the standard deviation of localid="1649489127059" . Show your method.
(c) How do the variance of localid="1649489132289" and the variance oflocalid="1649489138146" compare? Justify your answer.
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.
Better readers?() Did students have higher reading scores after participating in the chess program? Give appropriate statistical evidence to support your answer.
Running a mile A study of able-bodied male students at the University of Illinois found that their times for the mile run were approximately Normal with mean minutes and standard deviation minute. Choose a student at random from this group and call his time for the mile . Find and interpret the result. Follow the four-step process.
7. Benford鈥檚 law Refer to Exercise 5. The first digit of a randomly chosen expense account claim follows Benford鈥檚 law. Consider the events A = first digit is 7 or greater and B = first digit is odd.
(a) What outcomes make up the event A? What is P(A)?
(b) What outcomes make up the event B? What is P(B)?
(c) What outcomes make up the event 鈥淎 or B鈥�? What is P(A or B)? Why is this probability not equal to P(A) + P(B)?
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