Solved Problem 2-1 In the past 30 days, Roger’s Rural Roundup has sold 8, 9, 10, or 11 lottery tickets. It never sold fewer than 8 or more than 11. Assuming that the past is similar to the future, find the probabilities for the number of tickets sold if sales were 8 tickets on 10 days, 9 tickets on 12 days, 10 tickets on 6 days, and 11 tickets on 2 days.
SALES | NO. DAYS | PROBABILITY |
---|---|---|
8 | 10 | 0.333 |
9 | 12 | 0.400 |
10 | 6 | 0.200 |
11 | 2 | 0.067 |
Total | 30 | 1.000 |
Solved Problem 2-2 A class contains 30 students. Ten are female (F) and U.S. citizens (U); 12 are male (M) and U.S. citizens; 6 are female and non-U.S. citizens (N); 2 are male and non-U.S. citizens.
A name is randomly selected from the class roster, and it is female. What is the probability that the student is a U.S. citizen?
Solved Problem 2-3 Your professor tells you that if you score an 85 or better on your midterm exam, then you have a 90% chance of getting an A for the course. You think you have only a 50% chance of scoring 85 or better. Find the probability that both your score is 85 or better and you receive an A in the course.
Solved Problem 2-4 A statistics class was asked if it believed that all tests on the Monday following the football game win over their archrival should be postponed automatically. The results were as follows:
Strongly agree | 40 |
Agree | 30 |
Neutral | 20 |
Disagree | 10 |
Strongly disagree | 0 |
100 |
Transform this into a numeric score, using the following random variable scale, and find a probability distribution for the results:
Strongly agree | 5 | |
Agree | 4 | |
Neutral | 3 | |
Disagree | 2 | |
Strongly disagree | 1 |
OUTCOME | PROBABILITY, P (X) |
---|---|
Strongly agree (5) | 0.4 40 100 |
Agree (4) | 0.3 30 100 |
Neutral (3) | 0.2 20 100 |
Disagree (2) | 0.1 10 100 |
Strongly disagree (1) | 0.0 0 100 |
Total | 1.0 100 100 |
Solved Problem 2-5 For Solved Problem 2-4, let X be the numeric score. Compute the expected value of X.
Solved Problem 2-6 Compute the variance and standard deviation for the random variable X in Solved Problems 2-4 and 2-5.
The standard deviation is
Solved Problem 2-7 A candidate for public office has claimed that 60% of voters will vote for her. If 5 registered voters were sampled, what is the probability that exactly 3 would say they favor this candidate?
We use the binomial distribution with and
Solved Problem 2-8 The length of the rods coming out of our new cutting machine can be said to approximate a normal distribution with a mean of 10 inches and a standard deviation of 0.2 inch. Find the probability that a rod selected randomly will have a length
of less than 10.0 inches.
between 10.0 and 10.4 inches.
between 10.0 and 10.1 inches.
between 10.1 and 10.4 inches.
between 9.6 and 9.9 inches.
between 9.9 and 10.4 inches.
between 9.886 and 10.406 inches.
First, compute the standard normal distribution, the Z value:
Next, find the area under the curve for the given Z value by using a standard normal distribution table.