91影视

In a recent poll, the Gallup Organization found that \(45 \%\) of adult Americans believe that the overall state of moral values in the United States is poor. (a) Compute the mean and standard deviation of the random variable \(X,\) the number of adults who believe that the overall state of moral values in the United States is poor based on a random sample of 500 adult Americans. (b) Interpret the mean. (c) Would it be unusual to identify 240 adult Americans who believe that the overall state of moral values in the United States is poor based on a random sample of 500 adult Americans? Why?

Historically, the probability that a passenger will miss a flight is 0.0995. Source: Passenger-Based Predictive Modeling of Airline No-show Rates by Richard D. Lawrence, Se June Hong, and Jacques Cherrier. Airlines do not like flights with empty seats, but it is also not desirable to have overbooked flights because passengers must be "bumped" from the flight. The Lockheed L49 Constellation has a seating capacity of 54 passengers. (a) If 56 tickets are sold, what is the probability 55 or 56 passengers show up for the flight resulting in an overbooked flight? (b) Suppose 60 tickets are sold, what is the probability a passenger will have to be "bumped"? (c) For a plane with seating capacity of 250 passengers, how many tickets may be sold to keep the probability of a passenger being "bumped" below \(1 \% ?\)

A probability distribution for the random variable \(X,\) the number of trials until a success is observed, is called the geometric probability distribution. It has the same criteria as the binomial distribution (see page 328 ), except that the number of trials is not fixed. Its probability distribution function (pdf) is $$ P(x)=p(1-p)^{x-1}, \quad x=1,2,3, \ldots $$ where \(p\) is the probability of success. (a) What is the probability that Shaquille O'Neal misses his first two free throws and makes the third? Over his career, he made \(52.4 \%\) of his free throws. That is, find \(P(3)\) (b) Construct a probability distribution for the random variable \(X,\) the number of free-throw attempts of Shaquille O'Neal until he makes a free throw. Construct the distribution for \(x=1,2,3, \ldots, 10 .\) The probabilities are small for \(x>10\) (c) Compute the mean of the distribution, using the formula presented in Section 6.1 (d) Compare the mean obtained in part (c) with the value \(\frac{1}{p}\). Conclude that the mean of a geometric probability distribution is \(\mu_{X}=\frac{1}{p} .\) How many free throws do we expect Shaq to take before we observe a made free throw?

State the criteria for a binomial probability experiment.

Explain what 鈥渟uccess鈥� means in a binomial probability experiment.

Explain how the value of \(p,\) the probability of success, affects the shape of the distribution of a binomial random variable.