107.The average wait time at a McDonald’s drive-through window is about three minutes (“The Doctor Will See You Eventually,” The Wall Street Journal, October 18, 2010). What is the probability that a taxi arrives in three minutes or less? observations that fall between and is closest to . 30. The mean of a continuous uniform distribution is simply the average of the upper and lower limits of the interval on which the distribution is defined. Suppose the return for the following year follows a normal distribution, with the historical mean and standard deviation. The East Los Angeles Interchange is the busiest freeway interchange in the world. 85. 5. The probability mass function (pmf) (or frequency function) of a discrete random variable \(X\) assigns probabilities to the possible values of the random variable. In this post, I collected definitions of the basic probability theory concepts in the language of measure theory, following Kolmogorov, with a bit of modern terminology and emphasis on intuition behind them. What is the proportion of the houses that are worth more than $2.5 million? The service time is exponentially distributed with a mean of four minutes. The filling machine drops between 13.5 and 15 ounces of crackers into each box. Refer to Exhibit 6-3. B. 47. What is the probability that the battery will last more than 9 hours before running out of power? Suppose the wait time is exponentially distributed. An investment consultant tells her client that the probability of making a positive return with her suggested portfolio is 0.90. Which of the following is true about the z value corresponding to a given x value? a. 75. D. About a 95% chance that the actual return will fall within -4% and 28%. In 2006, the mean U.S. household income was approximately $50,000. C. The tails get closer and closer to the x axis and eventually cross this axis. How is the, 38. Assume the amount of gold found per 1000 tons of dirt is normally distributed. 57. The probability density function of a continuous uniform distribution is positive for all values between –∞ and +∞. True False. Her low-end estimate of net income is $250,000, and her high-end estimate is $350,000. 18. What are the mean and variance of this distribution? What is the probability a rider must wait more than 1.5 minutes? The relatively risky fund promises an expected return of 9%, with a standard deviation of 12%. He thinks his latest movie will be a huge hit. C.A continuous random variable has a probability mass function, and a discrete random variable has a. D.A continuous random variable has a probability density function, and a discrete random variable has a probability mass function. What is the probability that this bag will be warm enough on a randomly selected May night at the park? 93. 25. D. The number of customer arrivals to a bank between 10 am and 11 am. (Assume that the profit at the box office is normally distributed.). 62. A continuous random variable has the uniform distribution on the interval [a, b] if its probability density, C. Is constant for all x between a and b, and 0 otherwise, D. Asymptotically approaches the x axis when x increases to +∞ or decreases to –∞, 22. Refer to Exhibit 6-4. EXHIBIT 6-4. Let the time between two consecutive arrivals at a grocery store check-out line be exponentially distributed with a mean of three minutes. D. The tails get closer and closer to the x axis and eventually become this axis. 36. Refer to Exhibit 6-1. Examples of random variables that closely follow a normal distribution include the age and the class year designation of a college student. What can be said about the expected value and standard deviation of an exponential distribution?

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