Assume the following informaon. The height of adult women in the city of Boston can be characterized with a normal distribuon with mean 65 inches and standard deviaon 3 inches. The height of adult women in the city of Seoul can be characterized with a normal distribuon with mean 63 inches and standard deviaon 2 inches. Alice lives in Boston and is 66.5 inches tall. [1] Find the probability that a randomly chosen woman in the city of Boston is taller than Alice. [2] Assume you randomly choose 1 women from the city of Boston and 1 women from the city of Seoul. Find the probability that the women from Boston is taller than the women from Seoul. [3] How many women from the city of Seoul would you have to pick so that, with at least 95% probability, their average height is less that 1 inch above or below the populaon mean?

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 + ...