The mathematical statement of the uniform distribution is. Find the probability that the truck driver goes more than 650 miles in a day. It is _____________ (discrete or continuous). Alan Anderson, PhD is a teacher of finance, economics, statistics, and math at Fordham and Fairfield universities as well as at Manhattanville and Purchase colleges. Find the probability that a person is born after week 40. Sketch the graph, and shade the area of interest. Facts About the Chi-Square Distribution, 69. Skewness and the Mean, Median, and Mode, 16. With the uniform distribution, all values over an interval (a, b) are equally likely to occur. The Central Limit Theorem for Sample Means, 36. This means you will have to find the value such that , or 75%, of the cars are at most (less than or equal to) that age. What is the probability density function? Unlike a chi-square distribution, there is no skewness to a uniform distribution. The 90th percentile is 13.5 minutes. The total probability for any distribution is 1; therefore, the area under the rectangle must equal 1. What is the probability that a person waits fewer than 12.5 minutes? UNIFORM_INV(p, α, β) = x such that UNIFORM_DIST(x, α, β, TRUE) = p. Thus UNIFORM_INV is the inverse of the cumulative distribution version of UNIFORM_DIST. / Uniform distribution Calculates a table of the probability density function, or lower or upper cumulative distribution function of the uniform distribution, and draws the chart. The horizontal axis shows the range of values for X (0 to 10). The age of a first grader on September 1 at Garden Elementary School is uniformly distributed from 5.8 to 6.8 years. Ninety percent of the time, a person must wait at most 13.5 minutes. Find the probability that a randomly selected home has more than 3,000 square feet given that you already know the house has more than 2,000 square feet. The data follow a uniform distribution where all values between and including zero and 14 are equally likely. Find the probability that the value of the stock is between ?19 and ?22. Find the mean, μ, and the standard deviation, σ. b. μ = = = 7.5. We write X ∼ U(a, b). Find the probability that he lost less than 12 pounds in the month. What is the probability that the duration of games for a team for the 2011 season is between 480 and 500 hours? McDougall, John A. Use the following information to answer the next three exercises. X = a real number between a and b (in some instances, X can take on the values a and b). The height is. The graph of a uniform distribution is usually flat, whereby the sides and top are parallel to the x- and y-axes. Find the probability that the commuter waits less than one minute. On the average, how long must a person wait? A Confidence Interval for A Population Proportion, 42. in financial engineering from Polytechnic University. The data that follow are the number of passengers on 35 different charter fishing boats. Properties of Continuous Probability Density Functions, 32. A fireworks show is designed so that the time between fireworks is between one and five seconds, and follows a uniform distribution. Testing the Significance of the Correlation Coefficient, 72. The number of miles driven by a truck driver falls between 300 and 700, and follows a uniform distribution. X = The age (in years) of cars in the staff parking lot. Find the probability that the truck drivers goes between 400 and 650 miles in a day. Sketch the graph of the probability distribution. State the values of a and b. The distribution assigns a probability of 0 to any value of X outside of the interval from 0 to 10. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive of endpoints. The sample mean = 2.50 and the sample standard deviation = 0.8302. The Sky Train from the terminal to the rental–car and long–term parking center is supposed to arrive every eight minutes. A subway train on the Red Line arrives every eight minutes during rush hour. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive of endpoints. Considering only the cars less than 7.5 years old, find the probability that a randomly chosen car in the lot was less than four years old. On the average, a person must wait 7.5 minutes. b is 12, and it represents the highest value of x. The height of the rectangle equals 1 divided by the base (1/10 in this case). The mean of X is . Predicting with a Regression Equation, 74. The standard deviation of X is . Shade the area of interest. Types of Uniform Distribution Uniform distribution can be grouped into two categories based on the types of possible outcomes. Find the probability that the commuter waits between three and four minutes. Contingency Tables and Probability Trees, 26. The probability a person waits less than 12.5 minutes is 0.8333. b. a is zero; b is 14; X ~ U (0, 14); μ = 7 passengers; σ = 4.04 passengers. Sketch and label a graph of the distribution. The cumulative distribution function of X is P(X ≤ x) = . Use the following information to answer the next ten questions. What is the height of f(x) for the continuous probability distribution? If X has a uniform distribution where a < x < b or a ≤ x ≤ b, then X takes on values between a and b (may include a and b). σ = = 4.3. The Standard deviation is 4.3 minutes. Write the probability density function. The Central Limit Theorem for Proportions, 39. The height always equals 1 divided by the base; this ensures that the area of the rectangle always equals 1. What is the theoretical standard deviation? Instead, a continuous distribution may be illustrated with a line or a curve. The time follows a uniform distribution. That is, find.