Exam 8: Continuous Probability Distributions

The variance of a Student t distribution approaches ____________________ as the degrees of freedom increase to infinity.

If the random variable X is exponentially distributed and the parameter of the distribution λ = 4,then P(X ≤ 1)= 0.25.

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

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

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

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:

The probability density function of a uniform random variable on the interval [0,5] must be ____________________ for 0 ≤ x ≤ 5.

The variance of a χ² distribution is twice the value of its mean.

A standard normal distribution is a normal distribution with:

If the parameter of an exponential distribution is 1,then which of the following is true?

For values of degrees of freedom greater than 100,the ² distribution can be approximated by a(n)____________________ distribution.

If the mean of an exponential distribution is 2,then the value of the parameter λ is 2.0.

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.

If X is a continuous random variable on the interval [0,10],then P(X = 5)= f(5)= 1/10.

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 94 or lower?

The variance of a Student t random variable with v degrees of freedom (v > 2)is always greater than 1.

Use the F table to find the following values of F. a.F_.01,12,20 b.F_.05,20,40 c.F_.025,5,15 d.F_.01,8,30

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 probability that a randomly selected caller is placed on hold for fewer than 6 minutes?

If the mean of an exponential distribution is 2,then the value of the parameter λ is