Museum membership A museum offers several levelsof membership, as shown in the table.a) Find the mean and standard deviation of the donations.b) During their annual membership drive, they hope tosign up 50 new members each day. Would you expectthe distribution of the donations for a day to follow aNormal model? Explain.c) Consider the mean donation of the 50 new memberseach day. Describe the sampling model for thesemeans (shape, center, and spread). MemberCategoryAmount ofDonation ($)Percent ofMembersIndividual 50 41Family 100 37Sponsor 250 14Patron 500 7Benefactor 1000 1

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 + ...