According to Chebychev's theorem, the probability that the random variable Y differ from the mean u by less than 3 standard deviation is at least

Q: Suppose the random variable Z follows a standard normal distribution. Then the probability is 0.67…

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Q: Find the variance and standard deviation of the probability distribution of random variable X if :…

A: Variance=EX2-E2(X)=12110+22110+32110+42110+52110+62110+72110+82110+92110+102110-1110+2110+3110+4110+…

Q: Find the mean and standard deviation  of this random variable.

A: Define the Random Variable, X : Number of tickets bought by a individual Given that, X ~ Discrete…

Q: Suppose the random variable Xfollows a normal distribution with mean 30 and variance 81. Then the…

A: Given that a random variable X follows a normal distribution with mean 30 and variance 81. We have…

Q: Consider a uniform distribution from 1 to 8.  What is the probability that the random variable has a…

A: From the provided information, Let X be a random variable which follows uniform distribution. X ~U…

Q: Suppose the random variable Z follows a standard normal distribution. Then the probability is 0.20…

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Q: Suppose the random variable Z follows a standard normal distribution. Then the probability is 0.20…

A: Let us assume the probability that Z is less than K is 0.20 So we can write: P(Z<K)=0.20

Q: If Z is a random variable from a standard normal distribution and if P(Z<a)=0.42, then P(Z<-a)=0.58.…

A: If Z is a random variable from a standard normal distribution and if P(Z&lt;a)=0.42, then…

Q: Shirley Ferguson, an insurance broker, believes that for a particular contact the probability of…

A: Given: Probability of success (p) = 0.4 PX=x=0.4        x = 10.6        x =0 X ~ Bernoulli 0.4)

Q: The expected value of a random variable X that is denoted by u is called its: a. variance. O b.…

A: According to the given information, we haveRandom variable 'X' is given.

Q: If Z is a random variable from a standard normal distribution and if P(Z < a) = 0.7, then P(Z <= a)…

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Q: If z is a standard normal variable, find the probability when z is less than 1.98

A: Given that, Z score = 1.98 Left tailed

Q: Calculate the mean (mu)  and variance (sigma squared) of the probability distribution

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Q: Thestandard deviation of a probability distribution must be: A.anonnegative number B.anumber between…

A: The formula of standard deviation iss=Variance=∑x-x2n-1 Therefore, the value of standard deviation…

Q: The normal distribution is always used when the null hypothesis involves population mean.   A)…

A: Given: The normal distribution is always used when the null hypothesis involves population mean.

Q: if Z is a standard normal variable, find the probability the probability that Z is less than 1.13

A: Standardized z-score: The standardized z-score represents the number of standard deviations the data…

Q: The expected value of a random variable X that is denoted by u is called its: O a. variance. O b.…

A: The expected value of random variable X that is denoted by mu is called ?

Q: The expected value of a random variable X that is denoted by u is called its: O a. median. O b.…

A: The expected value of random variable X that is denoted by μ is called ?

Q: What is the probability that Z is equal to or smaller than 0.5? Z represents a standard normal…

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Q: Suppose a biologist is interested in monitoring the number of oak trees with oak wilt per acre. The…

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Q: if Z is a standard normal variable, find the probabilitythe probability that Z is greater than -1.82

A: Conclusion: The required  probability that Z is greater than -1.82 is 0.9656.

Q: The standard deviation of a continuous random variable is its expected value. O True O False

A: Given : The standard deviation of a continuous random variable is its expected value.

Q: For a Poisson random variable the mean and the standard deviation are the same. Select one: O True O…

A: If a random variable X~Poisson(λ) than f(x)=eλ λxx!; x≥0

Q: 3. Derive the variance of the F distribution.

A:

Q: The expected value of a random variable X that is denoted by u is called i O a. mean. O b. median.

A: The expected value of random variable X that is denoted by μ is called ?

Q: Given a survey conducted of randomly selected students, the number of credit course units that each…

A: Here , we know that number of students are countable. When we can count then it is discrete random…

Q: If Z is a standard normal​ variable, find the probability. The probability that Z is less than…

A: we hvae to find the probability.:_   The probability that Z is less than −0.25.

Q: Find the variance and standard deviation of the probability distribution of random variable X if…

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Q: When three coins are tossed once, the probability distribution for the random variable X…

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Q: f Z is a standard normal random variable, What is E[|z|]? Answer using four decimal places.

A: Z is a standard normal variable Z~N(0,1)   E(Z)=∫-∞∞z·12π e-z22dz=∫-∞0-z·12π e-z22dz+∫0∞z·12π…

Q: Assume that the random variable X is distributed, with mean 48 and standard deviation 11. Compute…

A: Given: Calculate the corresponding Z score as follows: The probability that the score is less than…

Q: The mean value of the Gaussian probability distribution is numerically equal to its variance. True…

A: The Gaussian probability distribution has two parameters mean and variance.

Q: Calculate the expected value, the variance, and standard deviation where X is the number of tails…

A: X=the number of tails n=sample size=3p=probability of success=12=0.5So, X follows a binomial…

Q: What is the probability of randomly selecting a z-score less than z = +2.25 from a normal…

A: A standard normal variable z follows normal distribution with mean 0 and standard deviation 1.

Q: The expected value of a random variable X that is denoted by u is called its: O a. median. O b.…

A: Correct answer is (c) Mean

Q: If Z is a random variable from a standard normal distribution and if P(Z > c) = 0.39, then P(Z < -…

A: In question,  Given that, Z is a random variable from a standard normal distribution. And pr(Z &gt;…

Q: If X is a normal random variable with a mean of 5000 and a variance of 100, then the standard random…

A: Given data: X follows normal distribution   Mean=5000 Variance=100   X~ Normal (5000, 100)

Q: Give the percent of scores between the mean and the z-value of normally distributed random variable.…

A: The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ  are the mean…

Q: b) Explain why the statistical properties of a random variable (RV) is expected to change if RV is…

A: The answer is explained below as follows.

Q: Find the standard deviation of the random variable X with the given probability distribution. * 1 2…

A: For the given data S.D =?

Q: Let X distributed as a Normal random variable with a mean of 15 and a standard deviation of  3. A)…

A: Solution: A. Let X be the random variable. From the given information, X follows normal distribution…

Q: For a Bernoulli random variable with probability of success P = 0.5, compute the mean and variance.

A: Let X denote the Bernoulli random variable. Probability of success (p)=0.5

Q: State the name of the random variable below a) number of positive results when testing 100 cattle…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: True or false For a normally distributed random variable, P(X > µ) = .5

A: The question is based on a normal dist. Given : P ( X &gt; μ ) = 0.5

Q: The central limit theorem states that the distribution of the mean of independent, identically…

A: Given that, random variable is independent and identically distributed.

Q: For a standard normal random variable, find the probability that z- exceeds the value -1.65.

A:

Q: Determine the standard deviation of the random variable, B(600,0.4).

A: Here we need to find the standard deviation of the given binomial random variable.