Random Variable Problems & Solutions

The following two-way contingency table gives the breakdown of the population of adults in a particular locale according to highest level of education and whether or not the individual regularly takes dietary supplements:
An adult is selected at random. Find the probability of each of the following events.
a. The person has a high school diploma and takes dietary supplements regularly.
b. The person has an undergraduate degree and takes dietary supplements regularly.
c. The person takes dietary supplements regularly.
d. The person does not take dietary supplements regularly.

Jesus011879 2022-08-22

Jamarcus Schroeder 2022-08-20

Find the following probabilities for a standard normal random variable z : P(-2.16<= z<=.55)

Leonidas Cook 2022-08-20

A population is normally distributed with $μ = 100$ and $σ = 25$ .
Find the probability that a value randomly selected from this population will have a value less than 95.

Macy Villanueva 2022-08-20

In the case of Standard Normal Distribution, the probability value that a random variable assume a value between 7 and 12 is similar to the probability value that a random variable assume a value from 7 to 12. Why is it so?

onetreehillyg 2022-08-20

If the range of X is the set {0, 1, 2, 3, 4} and P(X = x) = 0.2, determine the mean and variance of the random variable.

dejanimaab 2022-08-20

Find the following probabilities for a standard normal random variable z : P(-2<= z <= 2)

Tamara Anthony 2022-08-20

Find the following probabilities for a standard normal random variable z : P(z< 1)

Karli Kidd 2022-08-20

Find the following probabilities for a standard normal random variable z : P(z=1)

Licinilg 2022-08-20

Let X and Y be continuous random variables with joint density function
$f (x, y) = {\begin{array}{ll} \frac{x}{5} + c y & 0 < x < 1, 1 < y < 5 \\ 0 & o t h e r w i s e \end{array}$
where c is a constant. What is the value of c?

onetreehillyg 2022-08-20

The number of viewers of American Idol has a mean of 29 million with a standard deviation of 5 million. Assume this distribution follows a normal distribution. What is the probability that next week’s show will:
Exceed 40 million viewers?

Johan Patton 2022-08-19

Find the following probabilities for a standard normal random variable z :
$P (- .42 < z < 1.96)$

Nashorn0o 2022-08-19

A sample of 3 items is selected at random from a box containing 20 items of which 4 are defective. Find the expected number of defective items in the sample.

enseignement20 2022-08-19

Suppose that X is a random variable with mean and variance both equal to 20. What can be said about P{0<X<40}?

Cristal Travis 2022-08-19

The random variable x is normally distributed with mean
$μ = 174$
and standard deviation
$σ = 20$
Find the indicated probability. P(x > 182)

Zaiden Soto 2022-08-19

Suppose that a die is rolled twice. What are the possible values that the following random variables can take on: (a) the maximum value to appear in the two rolls; (b) the minimum value to appear in the two rolls; (c) the sum of the two rolls; (d) the value of the first roll minus the value of the second roll?

cronaficsiiilm 2022-08-19

A population is normally distributed with $μ = 100$ and $σ = 25$ .
Find the probability that a value randomly selected from this population will have a value between 95 and 135.

Angeline Avila 2022-08-18

Let X and Y be continuous random variables with joint density function
$f (x, y) = {\begin{array}{ll} \frac{x}{5} + c y & 0 < x < 1, 1 < y < 5 \\ 0 & o t h e r w i s e \end{array}$
where c is a constant. Find P(X+Y>3).

Zoie Frazier 2022-08-18

The time (in hours) required to repair a machine is an exponentially distributed random variable with parameter $λ = 1$ .
What is the probability that a repair time exceeds 2 hours?

ximblajy 2022-08-18

The number of viewers of American Idol has a mean of 29 million with a standard deviation of 5 million. Assume this distribution follows a normal distribution. What is the probability that next week’s show will:
Have at least 23 million viewers?

When you have an equation that deals with random variables, always start with an explanation related to some random variable examples. It is what the majority of skilled engineers do because it is the only way how one can avoid mistakes when working with statistical data. Even though this part of statistics and probability may seem overly complex, approach every random variable equation through the lens of probability as you seek answers to your questions. Compare provided solutions, see similarities, and you will achieve the most efficient solutions.

Explore Random Variables: Examples & Equations