The annual per capita consumption of fresh bananas​ (in pounds) in the United States can be approximiated by the normal​ distribution, with a mean of 10.4 pounds and a standard deviation of 1 pound. Answer the following questions about the specified normal distribution. (a) What is the smallest annual per capita consumption of bananas that can be in the top 10% of​ consumptions? (b) b) What is the largest annual per capita consumption of bananas that can be in the bottom 5% of​ consumption? (a) The smallest annual per captita consumption of bananas that can be in the top 10​% of consumptions is ______ pounds.  (Round to one decimal place as​ needed.) (b) The largest annual per capita consumption of bananas that can be in the bottom 5% of consumptions is_____  pounds. ​ (Round to one decimal place as​ needed.)

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 + ...