Question

An appliance dealer sells three different models of upright freezers having 12.5, 17.9, 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	p(x)
12.5	0.2
17.9	0.5
21.1	0.3

(a) Calculate the mean and standard deviation of x. (Round your answers to three decimal places.)

mean	cubic ft
standard deviation	cubic ft

(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 by the next customer?
mean $

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

Answer 1

a)

Mean = $\sum$ X * P(X)

= 12.5 * 0.2 + 17.9 * 0.5 + 21.1 * 0.3

= 17.78

Standard deviation = sqrt [ X² * P(X) - mean² ]

= sqrt [ 12.5² * 0.2 + 17.9² * 0.5 + 21.1² * 0.3 - 17.78² ]

= 2.982

b)

Price = 25X - 8.5

Mean = E(25 X - 8.5)

= 25 E(X) - 8.5

= 25 * 17.78 - 8.5

= 436

c)

Standard deviation = sqrt [ Var{25 X - 8.5 ]

= sqrt [ 25² * var{X) ]

= sqrt [ 25² * 2.982² ]

= 74.55