### MAT 119 8.4 The Binomial Distribution

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A+ TUTORIAL WITH WORK SHOWN FOR THE FOLLOWING QUESTIONS

1. Use the formula C(n, x)pxqn ? x to determine the probability of the given event. (Round your answer to four decimal places.)

The probability of exactly no successes in eight trials of a binomial experiment in which p = 1/4

1. Use the formula C(n, x)pxqn ? x to determine the probability of the given event. (Round your answer to four decimal places.)

The probability of at least two successes in four trials of a binomial experiment in which

p = 1/2

1. A fair die is rolled four times. Calculate the probability of obtaining exactly two 1s. (Round your answer to four decimal places.)

2. Let X be the number of successes in six independent trials of a binomial experiment in which the probability of success is

p = 4/5

(a)

P(X = 5)

(b)

P(2 ? X ? 5)

1. Let the random variable X denote the number of girls in a five-child family. If the probability of a female birth is 0.5, find the following probabilities.

(a) Find the probability of 0, 1, 2, 3, 4, and 5 girls in a five-child family. (Round your answers to three decimal places.)

P(0 girls) =

P(1 girl) =

P(2 girls) =

P(3 girls) =

P(4 girls) =

P(5 girls) =

(b) Construct the binomial distribution, and draw the histogram associated with this experiment.

(c) Compute the mean and the standard deviation of the random variable X. (Round your standard deviation to three decimal places.)

1. From experience, the manager of Kramer's Book Mart knows that 50% of the people who are browsing in the store will make a purchase. What is the probability that among ten people who are browsing in the store, at least five will make a purchase? (Round your answer to four decimal places.)

2. A biology quiz consists of fourteen multiple-choice questions. Nine must be answered correctly to receive a passing grade. If each question has four possible answers, of which only one is correct, what is the probability that a student who guesses at random on each question will pass the examination? (Round your answer to four decimal places.)

3. The probability that a DVD player produced by VCA Television is defective is estimated to be 0.07. A sample of ten players is selected at random. (Round your answers to four decimal places.)

(a) What is the probability that the sample contains no defective units?

(b) What is the probability that the sample contains at most two defective units?

1. As part of its quality-control program, the video-game DVDs produced by Starr Communications are subjected to a final inspection before shipment. A sample of nine DVDs is selected at random from each lot of DVDs produced, and the lot is rejected if the sample contains one or more defective DVDs. If 4.5% of the DVDs produced by Starr is defective, find the probability that a shipment will be accepted. (Round your answer to four decimal places.)

2. The probability that an airplane engine will fail in a transcontinental flight is 0.005. Assuming that engine failures are independent of each other, what is the probability that on a certain transcontinental flight, a four-engine plane will experience:

(a) Exactly one engine failure? (Round your answer to five decimal places.)

(b) Exactly two engine failures? (Round your answer to six decimal places.)

(c) More than two engine failures? (Note: In this event, the airplane will crash. Round your answer to nine decimal places.)

1. A new drug has been found to be effective in treating 70% of the people afflicted by a certain disease. If the drug is administered to 500 people who have this disease, what are the mean and the standard deviation of the number of people for whom the drug can be expected to be effective? (Round your standard deviation to two decimal places.)

2. At a certain university, the probability that an entering freshman will graduate within 4 years is 0.7. An incoming freshmen class has 2200 students.

(a) Find the expected number of students who will graduate within 4 years.

(b) Find the standard deviation of the number of students who will graduate within 4 years. (Round your answer to two decimal places.)

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