Probability of Different Scenarios

1. A study of 200 advertising firms revealed their income after taxes:

Income after Taxes Number of Firms
Under $1 million 102
$1 million to $20 million 61
$20 million or more 37

a. What is the probability an advertising firm selected at random has under $1 million in income after taxes?
b. What is the probability an advertising firm selected at random has either an income between $1 million and $20 million, or an income of $20 million or more? What rule of probability was applied?

2. A sample of 2,000 licensed drivers revealed the following number of speeding violations.

Number of Violations Number of Drivers
0 1,910
1 46
2 18
3 12
4 9
5 or more 5
Total 2,000

a. What is the experiment?
b. List one possible event.
c. What is the probability that a particular driver had exactly two speeding violations?
d. What concept of probability does this illustrate?

3. A normal population has a mean of 80.0 and a standard deviation of 14.0.

a. Compute the probability of a value between 75.0 and 90.0.
b. Compute the probability of a value 75.0 or less.
c. Compute the probability of a value between 55.0 and 70.0.

4. A recent study of the hourly wages of maintenance crew members for major airlines showed that the mean hourly salary was $20.50, with a standard deviation of $3.50. Assume the distribution of hourly wages follows the normal probability distribution. If we select a crew member at random, what is the probability the crew member earns:

a. Between $20.50 and $24.00 per hour?
b. More than $24.00 per hour?
c. Less than $19.00 per hour?