Checking Requirement The SAT test uses multiplechoice test questions, each with possible

Exact Value and Approximation Refer to Figure 621 in Example 2, and refer to the Minitab display near the beginning of this section. Figure 621 shows the shaded region representing exactly 235 wins among 431 games. What is the shape of the corresponding region in the Minitab display? If we use technology without an approximation, the probability of exactly 235 wins is found to be 0.0066. If we use the normal approximation to the binomial distribution, the probability of exactly 235 wins is found from Table A2 to be 0.0068. Which result is better? Is the approximation off by much?

Continuity Correction In a preliminary test of the MicroSort method of gender selection, 14 couples were treated and 13 of them had baby girls. If we plan to use the normal approximation to the binomial distribution for finding the probability of exactly 13 girls (assuming that the probability of a girl is 0.5), what is the continuity correction, and how would it be applied in finding that probability?

Notation The SAT test uses multiplechoice test questions, each with possible answers of a, b, c, d, e, and each question has only one correct answer. For people who make random guesses for answers to a block of 25 questions, identify the values of p, q, , and . What do and measure?

Checking Requirement The SAT test uses multiplechoice test questions, each with possible answers of a, b, c, d, e, and each question has only one correct answer. We want to find the probability of getting exactly 10 correct answers for someone who makes random guesses for answers to a block of 25 questions. If we plan to use the methods of this section with a normal distribution used to approximate a binomial distribution, are the necessary requirements satisfied? Explain

Using Normal Approximation. In Exercises 58, do the following: If the requirements of np 5 and nq 5 are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution if np < 5 or nq < 5 , then state that the normal approximation should not be used.With n = 13 and p = 0.4 , find P(fewer than 3).

Using Normal Approximation. In Exercises 58, do the following: If the requirements of np 5 and nq 5 are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution if np < 5 or nq < 5 , then state that the normal approximation should not be used.With n = 12 and p = 0.7 , find P(fewer than 8).

Using Normal Approximation. In Exercises 58, do the following: If the requirements of np 5 and nq 5 are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution if np < 5 or nq < 5 , then state that the normal approximation should not be used.With n = 20 and p = 0.8 , find P(more than 11).

Using Normal Approximation. In Exercises 58, do the following: If the requirements of np 5 and nq 5 are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution if np < 5 or nq < 5 , then state that the normal approximation should not be used.With n = 25 and p = 0.4 , find P(more than 9).

Voters. In Exercises 912, use a normal approximation to find the probability of the indicated number of voters. In each case, assume that 100 eligible voters aged 1824 are randomly selected. The most recent Census Bureau results show that among eligible voters aged 1824, 22% of them voted.Probability that fewer than 20 voted

Voters. In Exercises 912, use a normal approximation to find the probability of the indicated number of voters. In each case, assume that 100 eligible voters aged 1824 are randomly selected. The most recent Census Bureau results show that among eligible voters aged 1824, 22% of them voted.. Probability that at least 25 voted

Voters. In Exercises 912, use a normal approximation to find the probability of the indicated number of voters. In each case, assume that 100 eligible voters aged 1824 are randomly selected. The most recent Census Bureau results show that among eligible voters aged 1824, 22% of them voted. Probability of exactly 23 voters

Voters. In Exercises 912, use a normal approximation to find the probability of the indicated number of voters. In each case, assume that 100 eligible voters aged 1824 are randomly selected. The most recent Census Bureau results show that among eligible voters aged 1824, 22% of them voted.Probability of exactly 19 voters

Tennis Replay In the year that this exercise was written, there were 611 challenges made to referee calls in professional tennis singles play. Among those challenges, 172 were upheld with the call overturned. Assume that 30% of the challenges are successfully upheld with the call overturned. a. Find the probability that among the 611 challenges, the number of overturned calls is exactly 172. b. Of the 611 challenges, the number of 172 overturned calls is fewer than 30%. Find the probability that among the 611 challenges, the number of overturned calls is 172 or fewer. If the 30% rate is correct, is 172 overturned calls for 611 challenges an unusually low number? c. Which result is useful for determining whether the 30% rate is correct: part (a) or part (b)? Explain. d. Is there strong evidence to suggest that the rate of overturned calls is not 30%?

Tennis Replay Repeat the preceding exercise after changing the assumed rate of overturned calls from 30% to 33%.

Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 580 peas, with 428 of them having green pods. If we assume, as Mendel did, that under these circumstances, there is a 3 / 4 probability that a pea will have a green pod, we would expect that 435 of the peas would have green pods, so the result of 428 peas with green pods is fewer than expected. For the following, assume that the probability of a pea having a green pod is 3 / 4 . a. Find the probability that among the 580 offspring peas, exactly 428 of them have green pods. b. The result of 428 peas with green pods is fewer than 3 / 4 of 580. Find the probability that among the 580 offspring peas, 428 or fewer have green pods. Is the result of 428 peas with green pods unusually low? c. Which result is useful for determining whether Mendel's claimed rate of 75% is incorrect: part (a) or part (b)? Explain. d. Is there strong evidence to suggest that Mendel's probability of 3 / 4 is wrong?

Dream Job In a Marist College poll of 1004 adults, 291 chose professional athlete as their dream job. Assume that 25% of adults consider being a professional athlete their dream job. a. The result of 291 is more than 25% of 1004, so find the probability that among 1004 random adults, 291 or more consider being a professional athlete their dream job. b. If the value of 25% is correct, is the result of 291 unusually high? c. Does the result suggest that the rate is greater than 25%?

XSORT Gender Selection MicroSort's XSORT genderselection technique is designed to increase the likelihood that a baby will be a girl. In updated results (as of this writing) of the XSORT genderselection technique, 945 births consisted of 879 baby girls and 66 baby boys (based on data from the Genetics & IVF Institute). In analyzing these results, assume that the XSORT method has no effect so that boys and girls are equally likely.a. Find the probability of getting exactly 879 girls in 945 births. b. Find the probability of getting 879 or more girls in 945 births. If boys and girls are equally likely, is 879 girls in 945 births unusually high? c. Which probability is relevant for trying to determine whether the XSORT method is effective: the result from part (a) or the result from part (b)? d. Based on the results, does it appear that the XSORT method is effective? Why or why not?

Washing Hands Based on observed males using public restrooms, 85% of adult males wash their hands in a public restroom (based on data from the American Society for Microbiology and the American Cleaning Institute). In a survey of 523 adult males, 518 reported that they wash their hands in a public restroom. Assuming that the 85% observed rate is correct, find the probability that among 523 randomly selected adult males, 518 or more wash their hands in a public restroom. What do you conclude?

Voters Lying? In a survey of 1002 people, 701 said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that 61% of eligible voters actually did vote. Given that 61% of eligible voters actually did vote, find the probability that among 1002 randomly selected eligible voters, at least 701 actually did vote. What does the result suggest?

Cell Phones and Brain Cancer In a study of 420,095 cell phone users in Denmark, it was found that 135 developed cancer of the brain or nervous system. Assuming that the use of cell phones has no effect on developing such cancers, there is a 0.000340 probability of a person developing cancer of the brain or nervous system. We therefore expect about 143 cases of such cancers in a group of 420,095 randomly selected people. Estimate the probability of 135 or fewer cases of such cancers in a group of 420,095 people. What do these results suggest about media reports that cell phones cause cancer of the brain or nervous system?

Smoking Based on a recent Harris Interactive survey, 20% of adults in the United States smoke. In a survey of 50 statistics students, it is found that 6 of them smoke. Find the probability that should be used for determining whether the 20% rate is correct for statistics students. What do you conclude?

Smoking Repeat the preceding exercise after changing the results so that among 50 statistics students, it is found that 3 smoke.

Online TV In a Comcast survey of 1000 adults, 17% said that they watch primetime TV online. If we assume that 20% of adults watch primetime TV online, find the probability that should be used to determine whether the 20% rate is correct or whether it should be lower than 20%? What do you conclude?

Internet Access Of U.S. households, 67% have Internet access (based on data from the Census Bureau). In a random sample of 250 households,

Decision Theory Marc Taylor plans to place 200 bets of $5 each on a game at the Mirage casino in Las Vegas. a. One strategy is to bet on the number 7 at roulette. A win pays off with odds of 35:1 and, on any one spin, there is a probability of 1 / 38 that 7 will be the winning number. Among the 200 bets, what is the minimum number of wins needed for Marc to make a profit? Find the probability that Marc will make a profit. b. Another strategy is to bet on the pass line in the dice game of craps. A win pays off with odds of 1:1 and, on any one game, there is a probability of 244 / 495 that he will win. Among the 200 bets, what is the minimum number of wins needed for Marc to make a profit? Find the probability that Marc will make a profit. c. Based on the preceding results, which game is the better investment: the roulette game from part (a) or the craps game from part (b)? Why?

Overbooking a Boeing 767300 A Boeing 767300 aircraft has 213 seats. When someone buys a ticket for a flight, there is a 0.0995 probability that the person will not show up for the flight (based on data from an IBM research paper by Lawrence, Hong, and Cherrier). How many reservations could be accepted for a Boeing 767300 for there to be at least a 0.95 probability that all reservation holders who show will be accommodated?