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.

(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.

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 ...

The probability that a teenage driver will speed is 0.8; for a twenty-something driver, the probability of speeding is 0.5; for a mature driver, 0.2. Suppose that 15% of drivers are teenagers, 20% are in their twenties, and the rest are mature. If a driver observed at random is found to be speeding, then what is the probability

Let x determine a random variable, and user your knowledge of probability to prepare a probabilitydistribution.
Five cards are drawn(with replacement) and the number of red cards is noted. A probabilitydistributionfor the given experiment is as follows
x 0 1 2 3 4 5
P(x)_________________5___1

The probabilitydistributionfor the random variable x is as follows
x is 20 25 30 35
f(x) is .20 .15 .25 .40
a. Is this probabilitydistribution valid? Explain.
b. What is the probability that x=30?
c. What is the probability that x is less than or equal to 25?
d. What is the probability that x is greater than 30?

Three marbles are chosen without replacement from a box containing 12 red, 7 blue, and 8 yellow marbles. Let X be the number of blue marbles chosen.
a) Find and graph the probabilitydistribution of X.
b) Find the mean of the random variable X.

The proportion of individuals insured by the All-Driver Automobile Insurance Company who received at least one traffic ticket during a five-year period is .15.
1. Show the sampling distribution of p if a random sample of 150 insured individuals is used to estimate the proportion having received at least one ticket.
2. What i

Let x be a random variable with the following probabilitydistribution:
Value x of X......P(X = x)
........-1...............0.05
.........0...............0.05
.........1...............0.60
.........2...............0.05
.........3...............0.15
.........4...............0.10
Find the expectation E(X) an

Please refer to the attachment for the Joint Probability Table.
A. If a driver in this city is selected at random, what is the probability that he or she drives less than 10,000 miles per year or has a accident?
B. If a driver in this city is selected at random, what is the probability that he or she drives 10,000 or more

Question 1
A restaurant can serve up to 75 meals. Experience shows that 20% of clients who have booked do not turn up.
1. The manager accepts 90 bookings. What is the probability that more than 50 clients turn up?
2. How many bookings should the manager accept in order to have a probability of more than 0.9 that he will s