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STATISTICS AND PROBABILITY
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RANDOM VARIABLES
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Algebra
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Random variables
Sampling distributions
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Summarizing quantitative data
Analyzing categorical data
Modeling data distributions
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Comparing two groups
Alternate coordinate systems
Describing quantitative data
Chi-square tests
Two-way tables
Bivariate numerical data
Study design
Scatterplots
Upper level probability
Calculus and Analysis
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Random variables Answers
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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