Exam 7: Continuous Probability Distributions

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

Suppose f(x)= 1\4 over the range a £ x £ b , and suppose P ( X > 4)= 1\2. What are the values for a and b ?

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

Suppose X is a normal random variable with mean 70 and standard deviation 3. Then P ( X = 3)= ____________________.

The variance of a c ² distribution is twice the value of its mean.

If the value of Z is z = 99, that means you are at the 99^th percentile on the Z distribution.

We standardize a random variable by subtracting its ____________________ and dividing by its ____________________.

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

If X has a normal distribution with mean 60 and standard deviation 6, which value of X corresponds with the value z = 1.96?

{Electronics Test Narrative} Find the probability that a student will take exactly one hour to finish the test.

Let X be a normally distributed random variable with a mean of 12 and a standard deviation of 1.5. What proportions of the values of X are: a. less than 14 b. more than 8 c. between 10 and 13

What number corresponds to F _.025,3,5

Use the t -table to find the following values of t . a. t _.10,9 b. t _.10,20 c. t _.025,82 d. t _.05,196

A normal distribution is symmetric; therefore the probability of being below the mean is 0.50 and the probability of being above the mean is 0.50.

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

The sum of all values of f(x)over the range of [ a , b ] must equal one.

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.

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 exactly one hour?

If your golf score is 3 standard deviations below the mean, its corresponding value on the Z distribution is - 3.

Suppose X is a continuous random variable for X between a and b . Then its probability ____________________ function must non-negative for all values of X between a and b .