Question

An appliance dealer sells three different models of upright freezers having 14.5, 16.9, and 21.1 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	14.5	16.9	21.1
p(x)	0.2	0.5	0.3

(a) Calculate the mean (in cubic feet) of x.

Calculate the standard deviation (in cubic feet) of x. (Round your answer to three decimal places.)

(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 price paid (in dollars) by the next customer?

(c) What is the standard deviation of the price paid (in dollars)? (Round your answer to the nearest cent.)

Answer 1

a)

Mean = X * P(X)

= 14.5 * 0.2 + 16.9 * 0.5 + 21.1 * 0.3

= 17.68

Standard deviation = sqrt [ X² * P(X) - Mean² ]

= sqrt [ (14.5² * 0.2 + 16.9² * 0.5 + 21.1² * 0.3 ) - 17.68² ]

= 2.416

b)

Price = 25X - 8.5

E ( Price) = E( 25X - 8.5 )

= 25 E(X) - 8.5

= 25 * 17.68 - 8.5

= 433.5

c)

Var ( 25 X - 8.5 ) = 25² Var ( X)

= 625 * 2.416²

= 3648.16

SD(Price) = sqrt ( Var( 25X - 8.5) )

= sqrt ( 3648.16)

= 60.4