Question

1 the probability distribution of x, the number of defective tires on a randomly selected automobile checked at a certain inspection station, is given in the following table.

The probability distribution of x, the number of defective tires on a randomly selected automobile checked at a certain inspection station, is given in the following table.

x	0	1	2	3	4
p(x)	.53	.15	.08	.05	.19

(a) Calculate the mean value of x.
μ_x =  

(a) Calculate the mean value of x.
μ_x =  

(b) What is the probability that x exceeds its mean value?
P (x > μ_x) =

2 Consider a large ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Let x and y denote the number of cars and buses, respectively, carried on a single trip. Cars and buses are accommodated on different levels of the ferry, so the number of buses accommodated on any trip is independent of the number of cars on the trip. Suppose that x and y have the probability distributions shown below:

x	0	1	2	3	4	5
p(x)	0.05	0.11	0.24	0.29	0.20	0.11

y	0	1	2
p(y)	0.60	0.10	0.30

(a) Compute the mean and standard deviation of x. (Round the answers to three decimal places.)
Mean of x ___
Standard deviation of x ___

(b) Compute the mean and standard deviation of y. (Round the answers to three decimal places.)

Mean of y ___
Standard deviation of y ___

(c) Compute the mean and variance of the total amount of money collected in tolls from cars. (Round the answers to two decimal places.)
Mean of the total amount of money collected in tolls from cars $ __
Variance of the total amount of money collected in tolls from cars ___

(d) Compute the mean and variance of the total amount of money collected in tolls from buses. (Round the answers to one decimal place.)
Mean of the total amount of money collected in tolls from buses $ ___
Variance of the total amount of money collected in tolls from buses ___

(e) Compute the mean and variance of z = total number of vehicles (cars and buses) on the ferry. (Round the answers to two decimal places.)
Mean of z ___
Variance of z ___

(f) Compute the mean and variance of w = total amount of money collected in tolls. (Round the answers to one decimal place.)
Mean of w $ ___
Variance of w ___

3. An appliance dealer sells three different models of upright freezers having 13.5, 14.9, and 20.1 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)
13.5	0.2
14.9	0.5
20.1	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

Mean in Cubic ft ___

Standard deviation ___

(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