The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 minute. For this distribution ? = 0.5 and ? = 0.289. (a) Let x be the sample mean waiting time for a random sample of 17 individuals. What are the mean and standard deviation of the sampling distribution of x? (Round your answers to three decimal places.) ?x  =    ?x  =    (b) Answer part (a) for a random sample of 45 individuals. (Round your answers to three decimal places.) ?x  =    ?x  =    (c) Draw a picture of the approximate sampling distribution of x when n = 45. A graph has a horizontal axis with values from approximately −3.5 to 3.5. A symmetric curve with a single peak in the center of the graph is drawn over the horizontal axis. The curve enters the left of the graph at a height of nearly zero, rises to a peak over the value 0 on the horizontal axis, then decreases and exits the graph on the right at a height of nearly zero. A graph has a horizontal axis with values from approximately 0 to 1. The graph consists of two vertical line segments drawn over the horizontal axis values of 0.35 and 0.65 respectively. The vertical line segments touch the horizontal axis. A horizontal line segment is drawn connecting the tops of the two vertical line segments. A graph has a horizontal axis with values from approximately 0 to 1. The graph consists of two vertical line segments drawn over the horizontal axis values of 0 and 1 respectively. The vertical line segments touch the horizontal axis. A horizontal line segment is drawn connecting the tops of the two vertical line segments. A graph has a horizontal axis with values from approximately 0.35 to 0.65. A symmetric curve with a single peak in the center of the graph is drawn over the horizontal axis. The curve enters the left of the graph at a height of nearly zero, rises to a peak over the value 0.5 on the horizontal axis, then decreases and exits the graph on the right at a height of nearly zero.

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 + ...