Exam 8: Continuous Probability Distributions

____________________ the value of $\sigma$ in a normal distribution will make it wider.

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

The shape of a X² distribution is ____________________.

NARRBEGIN: Diet Diet Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 10 pounds and a standard deviation of 5 pounds.NARREND -If Z is a standard normal random variable, find the value z for which: a.the area between 0 and z is 0.3729 b.the area to the right of z is 0.7123 c.the area to the left of z is 0.1736 d.the area between -z and z is 0.6630

Let X be an exponential random variable with $\lambda$ = 1.50. Find the following: a.f(x) b.The y-intercept of f(x)

Most values of a standard normal distribution lie between:

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

Z_.025 is the value of Z such that the area to the ____________________ of Z is .9750.

If X has an exponential distribution, the possible values of X are from ____________________ to infinity.

Suppose X has a normal distribution with mean 70 and standard deviation 5. The 50^th percentile of X is 70.

A continuous random variable X has a uniform distribution between 10 and 20 (inclusive), then the probability that X falls between 12 and 15 is 0.30.

NARRBEGIN: Diet Diet Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 10 pounds and a standard deviation of 5 pounds.NARREND -{Diet Narrative} What proportion of the dieters lost more than 12 pounds?

NARRBEGIN: Calculus Scores Calculus Scores Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4. (Total possible points = 100.) NARREND -{Calculus Scores Narrative} What is the probability that a randomly selected student will have a score of 80 or higher?

The F distribution has two parameters called degrees of freedom, $\nu$ ₁ and $\nu$ ₂. We call $\nu$ ₁ the ____________________ degrees of freedom, and we call $\nu$ ₂ the ____________________ degrees of freedom.

A random variable X has a normal distribution with mean 132 and variance 36. If x = 120, its corresponding value of Z is 2.0.

Suppose you have a Student t distribution with 20 degrees of freedom. a.Find the mean. b.Find the variance. c.Find the standard deviation.

NARRBEGIN: Subway Waiting Time Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes.NARREND -{Subway Waiting Time Narrative} What is the probability of waiting no more than 3 minutes?

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} What is the median amount of time it takes a student to finish the test?

NARRBEGIN: Truck Salesman 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.NARREND -{Truck Salesman Narrative} What is the probability that he will have to wait between 6 and 10 days before making another sale?

Which of the following can have an exponential distribution?