1. Chapter 6 Extra Review

2. When people order books from a popular online source, they are shipped in standard-sized boxes. Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pounds, the mean weight of the packing material is 0.5 pounds with a standard deviation of 0.1 pounds, and the mean weight of the books shipped is 12 pounds with a standard deviation of 3 pounds. Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?
a) b) c) 3.02
d) e) 9.10

3. Which of the following is not a property of a binomial setting?
a) Outcomes of different trials are independent.
b) The chance process consists of a fixed number of trials, n.
c) The probability of success is the same for each trial.
d) If we use a sample size of 30, the binomial distribution will be approximately Normal.
e) Each trial can result in either a success or a failure.

4. A certain vending machine offers 20-ounce bottles of soda for $2
A certain vending machine offers 20-ounce bottles of soda for $2. The number of bottles X bought from the machine on any day is a random variable with mean 48 and standard deviation 7. Let the random variable Y equal the total revenue from this machine on a given day. Assume that the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?
a) μY = $2.00, σY = $14.00
b) μY = $50.00, σY = $9.00
c) μY = $96.00, σY = $14.00
d) μY = $50.00, σY = $2
e) μY = $96.00, σY = $2.00

5. Which of the following random variables is geometric?
a) The number of times I have to roll a die to get two 6s.
b) The number of cards I deal from a well- shuffled deck of 52 cards until I get a heart.
c) The number of digits I read in a randomly selected row of the random digits table until I find a 7.
d) The number of 7s in a row of 40 random digits.
e) The number of 6s I get if I roll a die 10 times.

6. A grocery chain runs a prize game by giving each customer a ticket that may win a prize when the box is scratched off. Printed on the ticket is a dollar value ($500, $100, $25) or the statement, “This ticket is not a winner.” Monetary prizes can be redeemed for groceries at the store. Here are the distribution of the prize values and the associated probabilities for each prize:
Which of the following are the mean and standard deviation, respectively, of the winnings?
a) $15.00, $ b) $15.00, $53.85
c) $15.00, $ d) $156.25, $53.85
e) $156.25, $26.93

7. Research suggests that about 54% of 12-year- olds in the United States can pick out the state of Colorado on a map.
a) What is the probability that you must sample exactly 5 twelve-year-olds to find the first one who can pick out Colorado on a map? Let C = the number of twelve-year olds it takes to be able to pick out Colorado on a map.
b) What is the probability that in a class of thirty 12-year olds, there are at least 25 that can pick out Colorado on a map? Let M = the number of twelve-year olds who are able to pick out Colorado on a map.  

8. The math and verbal SAT scores for 2016 can be considered normally distributed separate random variables. The mean and standard deviation for SAT math scores was 542 and 103 respectively. The mean and standard deviation for the verbal scores were 543 and 102 respectively. a) Find the expected overall SAT score for b) What is the standard deviation of the composite score for 2016? c) Find the probability that a student scores higher than a 1200 on the 2016 SAT.

9. Suppose we roll a fair die four times
Suppose we roll a fair die four times. The probability that a 6 occurs on exactly one of the rolls is
a) b)
c) d) e)

10. In a process for manufacturing glassware, glass stems are sealed by heating them in a flame. The temperature of the flame varies a bit. Here is the distribution of the temperature X measured in degrees Celsius:
a) Find the mean temperature µX.
b) Find the standard deviation σX.

11. In a process for manufacturing glassware, glass stems are sealed by heating them in a flame. The temperature of the flame varies a bit. Here is the distribution of the temperature X measured in degrees Celsius:
A manager asks for results in degrees Fahrenheit. The conversion of X into degrees Fahrenheit is given by
c) Find the mean temperature µY of the temperature of the flame in the Fahrenheit scale.
d) Find the standard deviation σY of the temperature of the flame in the Fahrenheit scale.

12. Hint: THIS IS LIKE THE EXTRA CREDIT PROBLEM
At a school with 600 students, 25% of them walk to school each day.
a) If we choose a random sample of 40 students, what is the expected number of students who will walk to school?
b) If we choose a random sample of 40 students, what is the standard deviation of the number of students who will walk to school?