Exam 8: Continuous Probability Distributions

P(Z > 1.9) = ____________________ P(Z < 1.9).

NARRBEGIN: Battery Life 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.NARREND -{Battery Life Narrative} What lifetime should the manufacturer advertise for these batteries in order that only 2% of the lamps will wear out before the advertised lifetime?

To find the probability for a uniform random variable you take the ____________________ times the ____________________ of its corresponding rectangle.

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

NARRBEGIN: Waiting Time 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.NARREND -{Waiting Time Narrative} What is the probability that a patient would have to wait exactly one hour?

A continuous random variable X has the following probability density function: f(x) = 1/4, 0 $\le$ x $\le$ 4 Find the following probabilities: a.P(X $\le$ 1) b.P(X $\ge$ 2) c.P(1 $\le$ X $\le$ 2) d.P(X = 3)

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

NARRBEGIN: Battery Life 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.NARREND -{Battery Life Narrative} What proportion of these batteries will last for more than 4,000 hours?

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 at least 8 days before making another sale?

Given that Z is a standard normal random variable, a negative value of Z indicates that the standard deviation of Z is negative.

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

NARRBEGIN: Waiting Time 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.NARREND -{Waiting Time Narrative} What is the probability density function for this uniform distribution?

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} If a dieter is selected at random, what is the probability that the dieter lost more than 7.5 pounds?

The 10^th percentile of a Z distribution has 10% of the Z-values lying above it.

Suppose X has a normal distribution with mean 10 and standard deviation 2. The probability that X is less than 8 is equal to the probability that Z is less than ____________________.

A random variable with density function 0.01e^-x/100 for x $\ge$ 0 has an exponential distribution whose mean is ____________________.

If X has an exponential distribution with parameter $\lambda$ , then the mean of X is ______________.

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

The value of $\chi$ ² with v degrees of freedom such that the area to its right under the chi-squared curve is equal to A is denoted by $\chi _ { A , v } ^ { 2 }$ , while $\chi _ { 1 - A , v } ^ { 2 }$ denotes the value such that the area to its left is A.

P(1 < Z < 2) = P(Z < 2) -____________________.