Exam 8: Continuous Probability Distributions

Truck Salesman A used truck salesman in a small town states that, on the average, it takes him 5 days to sell a truck.Assume that the probability distribution of the length of time between sales is exponentially distributed. -{Truck Salesman Narrative} What is the probability that he will have to wait between 6 and 10 days before making another sale?

A(n) ____________________ random variable has a density function that looks like a rectangle and you can use areas of a rectangle to find probabilities for it.

A normal distribution is symmetric; therefore the probability of being below the mean is 0.50 and the probability of being above the mean is 0.50.

Use the c² table to find the following values of c². a. b. c. d.

The probability density function f(x) of a random variable X that has a uniform distribution between a and b is

To be a legitimate probability density function, all possible values of f(x) must lie between 0 and 1 (inclusive).

Repair Time The time it takes a technician to fix a telephone problem is exponentially distributed with a mean of 15 minutes. -{Repair Time Narrative} What is the variance of the time it takes a technician to fix a telephone problem?

If the random variable X is exponentially distributed with parameter $\lambda$ = 3, then the probability P(X $\ge$ 2) equals:

A standard normal distribution is a normal distribution with:

Phone Orders The L.L.Bean catalog department that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. -{Phone Orders Narrative} What is the probability that a randomly selected caller is placed on hold for fewer than 6 minutes?

P(Z < 3.00) is approximately ____________________.

Most values of a standard normal distribution lie between:

Suppose X has a chi-squared distribution with 10 degrees of freedom.The mean of X is:

Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. -{Electronics Test Narrative} What is the median amount of time it takes a student to finish the test?

The exponential distribution is suitable to model the length of time that elapses before the first telephone call is received by a switchboard.

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. -{Battery Life Narrative} What proportion of these batteries will last less than 3,600 hours?

If the random variable X is exponentially distributed with parameter $\lambda$ = 0.05, then the variance of X, $\sigma$ ² = V(X) = 20.

What happens to the shape, mean, and variance of a Student t distribution as the degrees of freedom increase?

What number corresponds to F_.025,3,5?

In practice, we frequently use a continuous distribution to approximate a discrete one when the number of values the variable can assume is countable but large.