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Random variables

asked 2021-03-18

A population of values has a normal distribution with \(\displaystyle\mu={133.5}\) and \(\displaystyle\sigma={5.2}\). You intend to draw a random sample of size \(\displaystyle{n}={230}\).
Find the probability that a single randomly selected value is between 133.6 and 134.1.
\(\displaystyle{P}{\left({133.6}{<}{X}{<}{134.1}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

Random variables

asked 2021-03-09

A distribution of values is normal with a mean of 203.8 and a standard deviation of 50.2.
Find the probability that a randomly selected value is less than 113.4.
\(\displaystyle{P}{\left({X}{<}{113.4}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

Random variables

asked 2021-03-07

Give a counter example to the statement E(XY)=E(X)E(Y) implies
that X and Y are independent.

Random variables

asked 2021-03-07

A population of values has a normal distribution with \(\displaystyle\mu={182.5}\) and \(\displaystyle\sigma={49.4}\). You intend to draw a random sample of size \(\displaystyle{n}={15}\).
Find the probability that a sample of size \(\displaystyle{n}={15}\) is randomly selected with a mean greater than 169.7.
\(\displaystyle{P}{\left({M}{>}{169.7}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

Random variables

asked 2021-03-06

Are all infinite random variables necessary continuous?Explain.

Random variables

asked 2021-03-02

CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 271 dollars. You take a simple random sample of 96 auto insurance policies.
Find the probability that a single randomly selected value is less than 969 dollars.
\(\displaystyle{P}{\left({x}{<}{969}\right)}={P}{\left({x}{<}{969}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

Random variables

asked 2021-03-02

A population of values has a normal distribution with \(\displaystyle\mu={226.7}{\quad\text{and}\quad}\sigma={59.8}\). If a random sample size of n=24 is selected.
Find the probability that a single randomly selected value is greater than 192.5.

Random variables

asked 2021-03-02

Let X and Y be Bernoulli random variables. Let \(Z = XY\).
a) Show that Z is a Bernoulli random variable.
b) Show that if X and Y are independent, then \(P_{Z} = P_{X}P_{Y}\).

Random variables

asked 2021-03-01

A population of values has a normal distribution with mean 191.4 and standard deviation of 69.7. A random sample of size \(\displaystyle{n}={153}\) is drawn.
Find the probability that a sample of size \(\displaystyle{n}={153}\) is randomly selected with a mean between 188 and 206.6. Round your answer to four decimal places.
P=?

Random variables

asked 2021-02-26

Suppose that \(X_{1}, X_{2}, ..., X_{200}\) is a set of independent and identically distributed Gamma random variables with parameters \(\alpha = 4, \lambda = 3\).
Describe the normal distribution that would correspond to the sum of those 200 random variables if the Central Limit Theorem holds.

Random variables

asked 2021-02-25

A population of values has a normal distribution with \(\displaystyle\mu={192.6}\) and \(\displaystyle\sigma={34.4}\). You intend to draw a random sample of size \(\displaystyle{n}={173}\).
Find the probability that a sample of size \(\displaystyle{n}={173}\) is randomly selected with a mean less than 186.1.
\(\displaystyle{P}{\left({M}{<}{186.1}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

Random variables

asked 2021-02-25

Assume that there is a sampling distribution of \(\displaystyle\overline{{{x}}}\) of size 34 and they are selected at random from a normally distributed with a mean of 45 and a standard deviation of 6.2.
Find the probability that 1 randomly selected person has a value less than 40.

Random variables

asked 2021-02-25

Let \(\displaystyle{X}\sim{N}{\left({6},{4}\right)}\).Find the probabilities \(\displaystyle{P}{\left({X}{>}{8}\right)}\).

Random variables

asked 2021-02-25

Round each z-score to the nearest hundredth.
A data set has a mean of
\(\displaystyle{x}={6.8}\)
and a standard deviation of 2.5. Find the z-score.
\(\displaystyle{x}={7.2}\)

Random variables

asked 2021-02-25

Provide the formula for mean all symbols.

Random variables

asked 2021-02-24

A population of values has a normal distribution with \(\displaystyle\mu={73.1}\) and \(\displaystyle\sigma={28.1}\). You intend to draw a random sample of size \(\displaystyle{n}={131}\).
Find the probability that a single randomly selected value is greater than 69.7.
\(\displaystyle{P}{\left({X}{>}{69.7}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

Random variables

asked 2021-02-24

A normal population has mean \(\displaystyle\mu={20}\) and standard deviation \(\displaystyle\sigma={4}\).
What is the probability that a randomly chosen value will be greater than 25?

Random variables

asked 2021-02-21

A population of values has a normal distribution with \(\displaystyle\mu={116.5}\) and \(\displaystyle\sigma={63.7}\). You intend to draw a random sample of size \(\displaystyle{n}={244}\).
Find the probability that a single randomly selected value is between 104.7 and 112.8.
\(\displaystyle{P}{\left({104.7}{<}{X}{<}{112.8}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

Random variables

asked 2021-02-21

A population of values has a normal distribution with \(\displaystyle\mu={221.6}\) and \(\displaystyle\sigma={44.1}\). You intend to draw a random sample of \(\displaystyle{s}{i}{z}{e}{n}={42}\).
Find the probability that a single randomly selected value is between 221.6 and 229.1.
\(\displaystyle{P}{\left({221.6}{<}{X}{<}{229.1}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

Random variables

asked 2021-02-19

A population of values has a normal distribution with \(\displaystyle\mu={216.9}\) and \(\displaystyle\sigma={87.1}\). You intend to draw a random sample of size \(\displaystyle{n}={97}\).
Find the probability that a single randomly selected value is between 193 and 244.3.
\(\displaystyle{P}{\left({193}{<}{X}{<}{244.3}\right)}=\)?
Write your answers as numbers accurate to 4 decimal places.

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