Exam 8: Continuous Probability Distributions

Given that Z is a standard normal random variable, a negative value (z) on its distribution would indicate:

Given that Z is a standard normal random variable, the area to the left of a value z is expressed as

What happens to the shape, mean, and variance of a X² distribution as the degrees of freedom increase?

If X has an exponential distribution, then f(x) approaches ____________________ as x approaches infinity.

The number of parameters for an F distribution is:

NARRBEGIN: Phone Orders 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.NARREND -{Phone Orders Narrative} Find the waiting time at which only 10% of the customers will continue to hold.

A random variable with density function e^-x for x $\ge$ 0 has an exponential distribution with $\lambda$ = ____________________.

You can use a continuous random variable to ____________________ a discrete random variable that takes on a countable, but very large, number of possible values.

A random variable with density function e^-x for x $\ge$ 0 has an exponential distribution whose mean is ____________________.

If we standardize the normal curve, we express the original X values in terms of their number of standard deviations away from the mean.

NARRBEGIN: IT Graduates Salary IT Graduates Salary The recent average starting salary for new college graduates in IT systems is $47,500. Assume salaries are normally distributed with a standard deviation of $4,500.NARREND -{IT Graduates Salary Narrative} What is the cutoff for the top 3% of the salaries?

An exponential random variable is an example of a(n) ____________________ random variable.

Which of the following is always true for all probability density functions of continuous random variables?

Which of the following represents a difference between continuous and discrete random variables?

The mean of the standard normal distribution is ____________________ and the standard deviation is ____________________.

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.

NARRBEGIN: Phone Orders 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.NARREND -{Phone Orders Narrative} What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?

Use the F table to find the following probabilities. a.P(F_6,14 > 2.85) b.P(F_20,60 > 2.20) c.P(F_12,25 > 2.51) d.P(F_15,30 > 2.01)

NARRBEGIN: ElectronicsTest Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes.NARREND -{Electronics Test Narrative} Find the probability that a student will take no less than 55 minutes to finish the test.

The shape of an F distribution is ____________________.