Exam 8: Continuous Probability Distributions

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

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 density function for this uniform distribution?

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

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 $x _ { A , v } ^ { 2 }$ $\chi$ ² ,while $x^{2} _ { 1 - A } . { v }$ $\chi$ ² denotes the value such that the area to its left is A.

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. -{Diet Narrative} What proportion of the dieters gained weight?

The value of A such that P(-A $\le$ t $\le$ A)= 0.95,where the degrees of freedom are 20,is 2.086.

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

If P(t > t_.01,v)= 2.50,then the number of degrees of freedom v is:

A continuous random variable X has a uniform distribution between 5 and 25 (inclusive),then P(X = 15)= 0.05.

A c² distribution with 5 degrees of freedom has a mean of ____________________ and a variance of ____________________.

For values of degrees of freedom greater than 100,the c² distribution can be approximated by a(n)____________________ distribution.

What number corresponds to F_0.95,4,8?

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.

Suppose f(x)= 0.25.What range of possible values can X take on and still have the density function be legitimate?

If the random variable X is exponentially distributed with parameter $\lambda$ = 2,then the probability that X is between 1 and 2 equals the probability that X is between 2 and 3.

A standard normal distribution is a normal distribution with:

If the random variable X is exponentially distributed and the parameter of the distribution $\lambda$ = 4,then P(X $\le$ 1)= 0.25.

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 lifetime should the manufacturer advertise for these batteries in order that only 2% of the lamps will wear out before the advertised lifetime?

P(Z > 3.00)is approximately ____________________.

Suppose X has an F distribution.Which of the following is true?