In its Fuel Economy Guide, the Environmental Protection Agency gives a variety of data on 2016 model year vehicles. If outliers (hybrid, gas-electric or electric vehicles) are ignored, the combined city and highway gas mileage is approximately normally distributed with mean 23.0 mpg and standard deviation of 4.9 mpg. a) A 2016 Volkswagen Beetle has an average gas mileage of 28 mpg. What percentage of 2016 vehicles have a better mpg than the Volkswagen Beetle? b) What is the probability that a 2016 model year vehicle has a gas mileage lower than 30 mpg? c) Assume twenty 2016 model year vehicles are randomly selected. Describe the distribution of the variable ?̅. I. Shape. You must justify (state how you know) your answer. II. Mean. III. Standard deviation. Round to three decimal places. d) Find the probability that the mean gas mileage of a sample of twenty 2016 model year vehicles is less than 24 mpg.

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 + ...