BackAirline Reservations In Chapter 6, we learned that the proportion of passengers who miss a flight for which they have a reservation is 0.0995.
a. Suppose a flight has 290 reservations. What is the probability that 25 or more passengers will miss the flight?
Foreign Language According to a study done by Wakefield Research, the proportion of Americans who can order a meal in a foreign language is 0.47.
c. Describe the sampling distribution of p̂, the proportion of Americans who can order a meal in a foreign language. Be sure to verify the model requirements.
Foreign Language According to a study done by Wakefield Research, the proportion of Americans who can order a meal in a foreign language is 0.47.
e. Would it be unusual that, in a survey of 200 Americans, 80 or fewer Americans can order a meal in a foreign language? Why?
Airline Reservations In Chapter 6, we learned that the proportion of passengers who miss a flight for which they have a reservation is 0.0995. Suppose a flight has 320 reservations, but only 300 seats on the plane. What is the probability that 300 or fewer passengers show up for the flight?
Airline Reservations In Chapter 6, we learned that the proportion of passengers who miss a flight for which they have a reservation is 0.0995.
c. Suppose a popular flight has 300 seats and 300 reservations. Because this flight is popular, the proportion of passengers with a reservation who miss the flight is only 0.04. You are booked on a later flight and put yourself on the stand-by list. There are 14 passenger names ahead of you. What is the probability you get on this flight?
Entrepreneurship A Gallup survey indicated that 72% of 18- to 29-year-olds, if given a choice, would prefer to start their own business rather than work for someone else. A random sample of 600 18- to 29-year-olds is obtained today.
c. In a random sample of 600 18- to 29-year-olds, what is the probability that no more than 70% would prefer to start their own business?
Variability in Baseball Suppose, during the course of a typical season, a batter has 500 at-bats. This means the player has the opportunity to get a hit 500 times during the course of a season. Further, suppose a batter is a career 0.280 hitter (he averages 280 hits every 1000 at-bats or he has 280 successes in 1000 trials of the experiment), so the population proportion of hits is 0.280.
d. Explain why a career 0.280 hitter could easily have a batting average between 0.260 and 0.300.
Credit Cards According to creditcard.com, 29% of adults do not own a credit card.
a. Suppose a random sample of 500 adults is asked, “Do you own a credit card?” Describe the sampling distribution of p̂, the proportion of adults who do not own a credit card.
Acceptance Sampling A shipment of 50,000 transistors arrives at a manufacturing plant. The quality control engineer at the plant obtains a random sample of 500 resistors and will reject the entire shipment if 10 or more of the resistors are defective. Suppose that 4% of the resistors in the whole shipment are defective. What is the probability the engineer accepts the shipment? Do you believe the acceptance policy of the engineer is sound?
Social Security Reform A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 50 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of p̂, the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample if
a. 10% of all adult Americans support the changes?
Social Security Reform A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 50 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of p̂, the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample if
b. 20% of all adult Americans support the changes?
Peanut and tree nut allergies are considered to be the most serious food allergies. According to the National Institute of Allergy and Infectious Diseases, roughly 1% of Americans are allergic to peanuts or tree nuts. A random sample of 1500 Americans is obtained.
a. Explain why a large sample is needed for the distribution of the sample proportion to be approximately normal.
[DATA] Heights of Baseball PlayersData obtained from the National Center for Health Statistics show that men between the ages of 20 and 29 have a mean height of 69.3 inches, with a standard deviation of 2.9 inches. A baseball analyst wonders whether the standard deviation of heights of major-league baseball players is less than 2.9 inches. The heights (in inches) of 20 randomly selected players are shown in the table.
b. Compute the sample standard deviation.