An appliance dealer sells three different models of upright freezers having 14.5, 16.9, and 19.1 cubic feet of storage space. Let x = the amount of storage space purchased by the next customer to buy a freezer. Suppose that x has the following probability distribution.x p(x)14.5 .216.9 .519.1 .3(a) Calculate the mean and standard deviation of x.(b) If the price of the freezer depends on the size of the storage space, x, such that Price = 25x - 8.5, what is the mean value of the variable Price paid by the next customer?(c) What is the standard deviation of the price paid?
Accepted Solution
A:
Answer:17.08, 1.604Step-by-step explanation:given that an appliance dealer sells three different models of upright freezersas per data given below:x 14.5 16.9 19.1 Total
p 0.2 0.5 0.3 1
x*p 2.9 8.45 5.73 17.08
x^*p 42.05 142.805 109.443 294.298
Thus we find mean of X = 17.08Var(x) = [tex]294.298-17.08^2\\=2.5716[/tex]Std dev (x) = [tex]\sqrt{2.5716} \\=1.604[/tex]b) Price = 25x-8.5E(price) = [tex]E(25x-8.5) = 25E(x) -8.5\\= 418.50[/tex]c) Var (price) = [tex]Var(25x-8.5)\\= var(25x)\\=625 Var(x)\\sd (price)\\=25 *sd x\\= 40.091[/tex]