You and your friend carpool to school. Your friend has promised that he will come pick you up at your place at 8am, but he is always late(!) The amount of time he is late (in minutes) is a continuous Uniform random variable between 3 and 11 minutes. Which of the following statements is/are true? CHECK ALL THAT APPLY. A. The standard deviation of the amount of time that your friend is late is at about 2.31 minutes. B. It is less likely that your friend is late for more than 10 minutes than he is late for less than 4 minutes. C. The mean amount of time that your friend is late is 7 minutes. D. None of the above

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...