Question

An appliance dealer sells three different models of upright freezers having 13.6, 15.8, and 19.3 cubic feet of storage space. Consider the random variable 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)
13.6	0.2
15.8	0.5
19.3	0.3

(a)

Calculate the mean and standard deviation of x (in cubic feet). (Hint: See Example 6.15. Round your standard deviation to four decimal places.)

μ_x

= cubic ft

σ_x

= cubic ft

(b)

Give an interpretation of the mean and standard deviation of x in the context of observing the outcomes of many purchases.

The mean represents the long run average storage type of freezer sold by this particular appliance dealer. The standard deviation represents a typical deviation in what type of freezer purchased deviates from the mean.The mean represents the long run average number of freezers sold by this particular appliance dealer. The standard deviation represents a typical deviation in how many freezers purchased deviates from the mean.    The mean represents the long run average storage space of freezers sold by this particular appliance dealer. The standard deviation represents a typical deviation in how much the storage space in freezers purchased deviates from the mean.The mean represents the long run average cost of freezers sold by this particular appliance dealer. The standard deviation represents a typical deviation in how much is spent on freezers purchased deviates from the mean.The mean represents the long run average distribution of freezers sold by this particular appliance dealer. The standard deviation represents a typical deviation in how much the distribution in freezers purchased deviates from the mean.

Answer 1

From the given probability distribution:

a. The mean of X is given by:

The standard deviation of X is:

b.

The mean represents the long run average storage space of freezers sold by this particular appliance dealer.

The standard deviation represents a typical deviation in how much the storage space in freezers purchased deviates from the mean.