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pp.100-113 fall 2009

pp.100-113 fall 2009 - 100 Re-cap for the Binomial...

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Re-cap for the Binomial Probability Distribution : The binomial probability distribution is a special case of a discrete probability distribution. The binomial random variable, x, arises from binomial ‘experiments’. In a binomial experiment, you have : n trials of the experiment Two possible outcomes for any one trial, one outcome is denoted a ‘success’, the other a ‘failure’ The probability of a ‘success’ is denoted p. The probability of a failure is denoted 1-p. The trials are independent Example : A study of illegal drinking activities at large colleges and universities showed that 25% of underage female students reported binge drinking at least once a month. Suppose that 15 female students at a large university are selected at random to complete an anonymous questionnaire about their drinking habits. a) What is the probability that none out of fifteen will report binge drinking at least once a month? b) What is the probability that at least four will report binge drinking at least once a month? c) What is the expected number out of fifteen who will report binge drinking at least once a month? d) What is the variance for the number out of fifteen who will report binge drinking at least once a month? e) The standard deviation? 100

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f) Suppose that a large public university has 10,000 female undergraduates. What is the expected number who report binge drinking at least once a month? The variance? The standard deviation? 101
Continuous Probability Distributions A discrete probability distribution can be depicted by a graph in which the random variable, x, is plotted on the horizontal axis and the probability for each possible value of x is plotted on the vertical axis. The sum of the probabilities for each possible value equals one. A continuous random variable has an infinite number of possible values in any given interval. If each possible value of a continuous random variable, x, had a positive probability attached to it, the sum of probabilities would equal infinity! So, how do we depict continuous probability distributions?

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pp.100-113 fall 2009 - 100 Re-cap for the Binomial...

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