(Solution) A Museum offers several levels of membership

A museum offers several levels of membership, as shown in the table.

a) Find the mean and standard deviation of the donations.
b) During their annual membership drive, they hope to sign up 50 new members each day. Would you expect the distribution of the donations for a day to follow a Normal model? Explain.
c) Consider the mean donation of the 50 new members each day. Describe the sampling model for these means (shape, center, and spread).

Solution – A museum offers several levels of membership

a) Find the mean and standard deviation of the donations.

We will first calculate the mean donation and then the standard deviation using the data provided.

Mean donation:

The formula for the mean (μ) is:

μ=∑(x_i​×p_i​).

Where x_i​ is the amount of donation and p_i​ is the percentage of members (converted into a decimal) corresponding to that amount.

μ = 50(0.41) + 100(0.37) + 250(0.14) + 500(0.07) + 1000(0.01) ≈ $137.50

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