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Chapter 5: Q 58. (page 311)
In a table of random digits such as Table D, each digit is equally likely to be any of or What is the probability that a digit in the
table is or greater? (a) (c) (e) (b) (d)
The correct option is (d) 3/10
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Probability models? In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate, that is, satisfies the rules of probability. If not, give specific reasons for your answer.
(a) Roll a die and record the count of spots on the up-face: P(1) = 0, P(2) = 1/6, P(3) = 1/3, P(4) = 1/3,
P(5) = 1/6, P(6) = 0.
(b) Choose a college student at random and record gender and enrollment status: P(female full-time) = 0.56, P(male full-time) = 0.44, P(female part-time) = 0.24, P(male part-time) = 0.17.
(c) Deal a card from a shuffled deck: P(clubs) = 12/52, P(diamonds) = 12/52, P(hearts) = 12/52,
P(spades) = 16/52.
Languages in Canada Canada has two official languages, English and French. Choose a Canadian at random and ask, “What is your mother tongue?”
Here is the distribution of responses, combining many separate languages from the broad Asia/Pacific region:Language: English French Asian/Pacific Other Probability: ?
(a) What probability should replace “?” in the distribution? Why?
(b) What is the probability that a Canadian’s mother tongue is not English?
(c) What is the probability that a Canadian’s mother tongue is a language other than English or French?
Is this valid? Determine whether each of the following simulation designs is valid. Justify your answer.
(a) According to a recent survey, of people aged and older in the United States are addicted to email. To simulate choosing a random sample of
people in this population and seeing how many of them are addicted to email, use a deck of cards. Shuffle the deck well, and then draw one card at a
time. A red card means that person is addicted to email; a black card means he isn’t. Continue until you have drawn cards (without replacement) for the sample.
(b) A tennis player gets of his second serves in play during practice (that is, the ball doesn’t go out of bounds). To simulate the player hitting second serves, look at pairs of digits going across a row in Table D. If the number is between and , the service is in; numbers between and indicate that the service is out.
Nickels falling over You may feel it’s obvious that the probability of a head tossing a coin is aboutbecause the coin has two faces. Such opinions are not always correct. Stand a nickel on the edge on a hard, flat surface. Pound the surface with your hand so that the nickel falls over. Do this time, and record the results.
(a) What’s your estimate for the probability that the
coin falls heads up? Why?
(b) Explain how you could get an even better estimate.
Brushing teeth, wasting water? A recent study reported that fewer than half of young adults turn off the water while brushing their teeth. Is the same true for teenagers? To find out, a group of statistics students asked an SRS of 60 students at their school if they usually brush with the water off. How many
students in the sample would need to say “No” to provide convincing evidence that fewer than half of the students at the school brush with the water off? The Fathom dot plot below shows the results of taking 200 SRSs of 60 students from a population in which the true proportion who brush with the
water off is 0.50.
(a) Suppose 27 students in the class’s sample say “No.” Explain why this result does not give convincing evidence that fewer than half of the school’s students brush their teeth with the water off.
(b) Suppose 18 students in the class’s sample say “No.” Explain why this result gives strong evidence that fewer than 50% of the school’s students brush
their teeth with the water off.
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