Exam 8: Continuous Probability Distributions

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} Find the probability that a student will take more than 60 minutes to finish the test.

The total area under f(x)for a continuous random variable must equal ____________________.

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

If the mean of an exponential distribution is 2,then the value of the parameter $\lambda$ is

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 probability that it will take a technician between 10 to 15 minutes to fix a telephone problem?

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 proportion of callers are put on hold longer than 3 minutes?

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 mean amount of time it takes a student to finish the test?

The mean of an exponential random variable is ____________________ the median.

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

If the random variable X is exponentially distributed with parameter $\lambda$ = 4,then the probability P(X $\le$ 0.25),up to 4 decimal places,is

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

If a point y lies outside the range of the possible values of a random variable X,then f(y)must equal zero.

Which of the following has a mean and variance that depend on degrees of freedom?

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. ) -{Calculus Scores Narrative} What is the probability that a randomly selected student will have a score of 80 or higher?

Probability for continuous random variables is found by finding the ____________________ under a curve.

Checking Accounts A bank has determined that the monthly balances of the checking accounts of its customers are normally distributed with an average balance of $1,200 and a standard deviation of $250. -{Checking Accounts Narrative} What proportion of customers have monthly balances between $950 and $1,075?

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 value of $\lambda$ ,the parameter of the exponential distribution in this situation?

Waiting Time The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. -{Waiting Time Narrative} What is the probability that a patient would have to wait between one and two hours?

In the exponential distribution,X takes on an infinite number of possible values in the given range.

If X has an exponential distribution,its ____________________ is equal to its ____________________.