Random Variable Problems & Solutions

For a population ( $μ = 100$ and $σ = 20$ ), find the X values. $z = + 1.50$ .

Lewis Harvey 2021-02-11

A population of values has a normal distribution with $μ = 116.3$ and $σ = 27.5$ . You intend to draw a random sample of size $n = 249$ .
Find the probability that a sample of size $n = 249$ is a randomly selected with a mean greater than 117.3.
$P (\overset{―}{X} > 117.3) =$ ?
Write your answers as numbers accurate to 4 decimal places.

Wierzycaz 2021-02-09

If X and Y are random variables and c is any constant, show that $E (X + Y) = E (X) + E (Y)$ .

sagnuhh 2021-02-09

If X and Y are random variables and c is any constant, show that $E (c) = c$ .

geduiwelh 2021-02-08

A population of values has a normal distribution with $μ = 204.3$ and $σ = 43$ . You intend to draw a random sample of size $n = 111$ .
Find the probability that a single randomly selected value is less than 191.2.
$P (X < 191.2) =$ ?
Find the probability that a sample of size $n = 111$ is randomly selected with a mean less than 191.2.
$P (M < 191.2) =$ ?
Write your answers as numbers accurate to 4 decimal places.

kuCAu 2021-02-06

Whether the statement is true or false.

Globokim8 2021-02-05

For a population with a mean of $μ = 100$ and a standard deviation of $σ = 20$ ,
Find the X values.
$z = + .75$ .

he298c 2021-02-05

A population of values has a normal distribution with $μ = 133.5$ and $σ = 5.2$ . You intend to draw a random sample of size $n = 230$ .
Find the probability that a sample of size $n = 230$ is randomly selected with a mean between 133.6 and 134.1.
$P (133.6 < \overset{―}{x} < 134.1) =$ ?
Write your answers as numbers accurate to 4 decimal places.

Khaleesi Herbert 2021-02-05

A population of values has a normal distribution with $μ = 181$ and $σ = 41.8$ . You intend to draw a random sample of size $n = 144$ .
Find the probability that a single randomly selected value is between 176.5 and 183.1.
$P (176.5 < M < 183.1) =$ ?
Write your answers as numbers accurate to 4 decimal places.

Joni Kenny 2021-02-05

For normal distribution with a mean of 278 and a standard deviation of 25, what is the Z value for a random value to be 185?

smileycellist2 2021-02-03

Find. Sum of probabilities of discrete random variables.

FizeauV 2021-02-02

A population of values has a normal distribution with $μ = 13.2$ and $σ = 5$ . You intend to draw a random sample of size $n = 60$ .
Find the probability that a single randomly selected value is between 11.5 and 14.
$P (11.5 < X < 14) =$ ?
Write your answers as numbers accurate to 4 decimal places.

Lewis Harvey 2021-01-31

What is the probability of the random occurrence of a value between 56 and 61 from a normally distributed population with mean 62 and standard deviation 4.5?

cistG 2021-01-31

For a population with a mean of $μ = 100$ and a standard deviation of $σ = 20$ ,
Find the X values.
$z = - .50$ .

Anish Buchanan 2021-01-31

Let $X \sim N (6, 4)$ .Find the probabilities $P (X < 3)$ .

ka1leE 2021-01-28

A population of values has a normal distribution with $μ = 197$ and $σ = 68$ . You intend to draw a random sample of size $n = 181$
Find the probability that a sample of size $n = 181$ is randomly selected with a mean between 198.5 and 205.6.
$P (198.5 < M < 205.6) =$ ?
Write your answers as numbers accurate to 4 decimal places.

opatovaL 2021-01-27

A population of values has a normal distribution with $μ = 154.5$ and $σ = 96.1$ . You intend to draw a random sample of size $n = 134$ .
Find the probability that a single randomly selected value is greater than 167.
$P (X > 167) =$ ?
Write your answers as numbers accurate to 4 decimal places.

SchachtN 2021-01-25

To Explain:Linearity of expectation of random variables.

Armorikam 2021-01-22

The expectation of the number of people getting their correct hats in the hat check problem, using linearity of expectations.
n persons receive n hats in a random fashion.
Formula used: By linearity of expectation function,
If $X_{1}, X_{2}, . . ., X_{n}$ are random variables, then
$E (X_{1}, + X_{2} +, . . . + X_{n}) = E (X_{1}) + E (X_{2}) + . . . + E (X_{n})$ (2)

midtlinjeg 2021-01-22

A population of values has a normal distribution with mean = 37.4 and standard deviation 77.4. If a random sample of size $n = 15$ is selected,
Find the probability that a single randomly selected value is greater than 53.4. Round your answer to four decimals.
$P (X > 53.4) =$ ?

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