Random Variable Problems & Solutions

Round each z-score to the nearest hundredth.
A data set has a mean of
$x = 6.8$
and a standard deviation of 2.5. Find the z-score.
$x = 6.2$

Aneeka Hunt 2020-11-30

Discrete or Continuous? II Identify the following as discrete or continuous random variables:
a. Increase in length of life attained by a cancer patient as a result of surgery
b. Tensile breaking strength (in pounds per square inch) of 1-inch-diameter steel cable
c. Number of deer killed per year in a state wildlife preserve

amanf 2020-11-30

A population of values has a normal distribution with $μ = 29.3$ and $σ = 65.1$ . You intend to draw a random sample of size $n = 142$ .
Find the probability that a sample of size n=142 is randomly selected with a mean between 27.7 and 35.3.
$P (27.7 < \overset{―}{X} < 35.3) =$ ?
Write your answers as numbers accurate to 4 decimal places.

Wribreeminsl 2020-11-29

A population of values has a normal distribution with $μ = 116.5$ and $σ = 63.7$ . You intend to draw a random sample of size $n = 244$ .
Find the probability that a sample of size $n = 244$ is randomly selected with a mean between 104.7 and 112.8.
$P (104.7 < M < 112.8) =$ ?
Write your answers as numbers accurate to 4 decimal places.

jernplate8 2020-11-23

Statistical Literacy When using the F distribution to test variances from two populations, should the random variables from each population be independent or dependent?

Lennie Carroll 2020-11-23

Are all continuous random variable necessarily infinite? Explain.

nitraiddQ 2020-11-22

Independent random variables $X_{1} and X_{2}$ are combined according to the formula $L = 3 \cdot X_{1} + 2 \cdot X_{2}$ .
If $X_{1} and X_{2}$ both have a variance of 2.0, what is the variance of L?

necessaryh 2020-11-17

If you have $λ = 4.2$ , what is the probability that $P (x < 2)$ ?

Annette Arroyo 2020-11-16

Let $X \sim N (6, 4)$ .Find the probabilities $P (5 < X < 7)$ .

CheemnCatelvew 2020-11-09

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 sample of size $n = 134$ is randomly selected with a mean greater than 167.
$P (M > 167) =$ ?
Write your answers as numbers accurate to 4 decimal places.

BolkowN 2020-11-08

A population of values has a normal distribution with mean 18.6 and standard deviation 57. If a random sample of size $n = 25$ is selected,
Find the probability that a sample of size $n = 25$ is randomly selected with a mean greater than 17.5 round your answer to four decimal places.
P=?

Wierzycaz 2020-11-05

A population of values has a normal distribution with $μ = 129.7$ and $σ = 7.7$ . You intend to draw a random sample of size $n = 10$ .
Find the probability that a single randomly selected value is less than 130.9.
$P (X < 130.9) =$ ?
Write your answers as numbers accurate to 4 decimal places.

waigaK 2020-11-02

A population of values has a normal distribution with $μ = 49$ and $σ = 79.5$ . You intend to draw a random sample of size $n = 84$ .
Find the probability that a single randomly selected value is greater than 72.4.
$P (X > 72.4) =$ ?
Write your answers as numbers accurate to 4 decimal places.

Wotzdorfg 2020-11-01

Round each z-score to the nearest hundredth.
A data set has a mean of
$x = 6.8$
and a standard deviation of 2.5. Find the z-score.
$x = 9.0$

Lewis Harvey 2020-11-01

The random variable x stands for the number of girls in a family of four children.
1) Build a table showing the probability distribution, then calculate the mean and standard deviation. (Hint: List the different possible outcomes.)
2) Is it unusual for a family of four children to consist of four girls?

Reggie 2020-11-01

The random variable X follows a normal distribution $? (20, 102)$ .
Find $F \in d P (? > 30)$ ,

Isa Trevino 2020-10-28

A population of values has a normal distribution with $μ = 200$ and $σ = 31.9$ . You intend to draw a random sample of size $n = 11$ .
Find the probability that a single randomly selected value is less than 226.9.
$P (X < 226.9) =$ ?
Write your answers as numbers accurate to 4 decimal places.

Anonym 2020-10-28

A distribution of values is normal with a mean of 166.1 and a standard deviation of 73.5.
Find the probability that a randomly selected value is between 151.4 and 283.7.
$P (151.4 < X < 283.7) =$ Incorrect
Write your answers as numbers accurate to 4 decimal places.

zi2lalZ 2020-10-27

Round each z-score to the nearest hundredth.
A data set has a mean of
$x = 6.8$
and a standard deviation of 2.5. Find the z-score.
$x = 5.0$

Dolly Robinson 2020-10-27

A population of values has a normal distribution with $μ = 192.3$ and $σ = 66.5$ . You intend to draw a random sample of size $n = 15$ .
Find the probability that a sample of size $n = 15$ is randomly selected with a mean less than 185.4.
$P (M < 185.4) =$ ?
Write your answers as numbers accurate to 4 decimal places.

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