# Statistics and Probability Exercises

See the attached file.

1. Of households in the United States, 18 million, or 17%, have three or more vehicles, as stated in USA Today (June 12, 2002), quoting the Census Bureau as the source.

(a) If two U.S. households are randomly selected, find the probability that both will have three or more vehicles. (Give your answer correct to four decimal places.)

(b) If two U.S. households are randomly selected, find the probability that neither of the two has three or more vehicles. (Give your answer correct to four decimal places.)

(c) If four households are selected, what is the probability that all four have three or more vehicles? (Give your answer correct to four decimal places.)

Problem # 16

A study was conducted to investigate the relationship between the cost, y (in tens of thousands of dollars), per unit of equipment manufactured and the number of units produced per run, x. The resulting equation for the line of best fit is given below, with x being observed for values between 10 and 200. If a production run was scheduled to produce 85 units, what would you predict the cost per unit to be in dollars?

= 7.87 ? 0.04x

Problem 17

A study was conducted to investigate the relationship between the resale price, y (in hundreds of dollars), and the age, x (in years), of midsize luxury American automobiles. The equation of the line of best fit was determined below.

= 173.9 ? 20.45x

(a) Find the resale value in dollars of such a car when it is 3 years old.

(b) Find the resale value in dollars of such a car when it is 6 years old.

(c) What is the average annual decrease in the resale price in dollars of these cars?

Problem # 7

Does studying for an exam pay off? The number of hours studied, x, is compared with the exam grade received, y.

x 4 7 4 5 1

y 60 75 75 80 90

(a) Complete the preliminary calculations: SS(x), SS(y), and SS(xy).

(SS(x)) wrong answer

(SS(y)) wrong answer

(SS(xy)) wrong answer

(b) Find r. (Give your answer correct to three decimal places.)

wrong answer.

#### Solution Preview

See answer in the Word document.

1. Of households in the United States, 18 million, or 17%, have three or more vehicles, as stated in USA Today (June 12, 2002), quoting the Census Bureau as the source.

(a) If two U.S. households are randomly selected, find the probability that both will have three or more vehicles. (Give your answer correct to four decimal places.)

For each household, the probability of having three or more vehicles is 0.17.

Since these two households are independent from each other,

The probability that both will have three or more vehicles p=0.17*0.17=0.0289.

(b) If two U.S. households are randomly selected, find the probability that neither of the two has three or more vehicles. (Give your answer correct to four decimal places.)

For each household, the probability of not having three or more ...

#### Solution Summary

The solution provides detailed explanation how to find out the binomial probability and regression equation.