According to a 2009 Reader's Digest article, people throw away approximately 11% of what they buy at the grocery store. Assume this is the true proportion and you plan to randomly survey 111 grocery shoppers to investigate their behavior. What is the probability that the sample proportion exceeds 0.08? Note: You should carefully round any intermediate values you calculate to 4 decimal places to match wamap's approach and calculations. Answer =  (Enter your answer as a number accurate to 4 decimal places.)    A manufacturer knows that their items have a normally distributed length, with a mean of 14.9 inches, and standard deviation of 3.1 inches. If 13 items are chosen at random, what is the probability that their mean length is less than 13.6 inches?

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 + ...