# Probability distribution for random driver

Choose an American driver at random and let the random variable X be the number of speeding tickets the driver has received in the last two years. The discrete probability distribution of X is shown.

Tickets 0 1 2 3 4 5

Probability 0.16 0.32 0.25 0.12 0.09 0.06

(2) Verify the two main requirements that make this a legitimate discrete probability distribution.

(6) Create a probability histogram for the random variable X.

(4) Explain in words what the probability P(Xââ?°¤2) means. What is the probability P(Xââ?°¤2)?

(3) Write the mathematical expression of the event that a randomly chosen driver has more than three speeding tickets in terms of the random variable X. What is the probability of this event?

(5) Compute and interpret E(X), the expected value of the random variable X.

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#### Solution Preview

See attached file.

The conditions of a discrete probability distribution are:

1) the outcomes are finite (which is true in our case, since we have only 6 outcomes)

2) the sum of probabilities equal to 1 (which is also true since 0.16 + 0.32 + 0.25 + 0.12 + 0.09 + 0.06 ...

#### Solution Summary

Probability distribution for random driver

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?