X has a standard normal distribution. Derive the mean, variance, cdf and pdf of |X|. Show working

Q: Assume that the scores of a college entry exam are normally distributed with a mean of 400 and a…

A: Given,mean(μ)=400standard deviation(σ)=60

Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard…

A:

Q: The R function rnorm(n,mean,sd) generates random numbers from a normal distribution. Use rnorm(100)…

A: In the R-programming, for generating the random number from the normal distribution, we use R…

Q: Using table below, find the variance for  licensed dogs per household in this county? Please show…

A: X012345P(X=x)0.590.110.090.070.02

Q: State the properties of s normal distribution.

A: Normal distribution- when mean is 0 and standard deviation is  1 is called standard normal…

Q: Which proportion of a normal distribution is located between z = 0 and z = +1.50?

A: Solution: Here, it is needed to find the proportion of a normal distribution is located between z=0…

Q: Normal distributions have a mean of 0 and a standard deviation of 1.0. True False

A: Normal distribution, also known as the Gaussian distribution, is a probability distribution that is…

Q: X is random variable with a normal distribution having a mean of 3 and variance of 2. Find P ( X> 4)…

A:

Q: Let X follow a normal distribution with mean 5.3 and unknown standard deviation. If P(X < 11.6) =…

A: From the given information, let X follows a normal distribution with mean of 5.3 and standard…

Q: he percentage of heights less tahn 169 centimeters is ________%.  Round to two decimal places as…

A: mean = 169 sigma = 7

Q: For a standard normal curve, find the probability a value has a z-score less than -2.

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

Q: c) the gestation time differs from the mean by more than 3 weeks. d) of 100 boys born in upstate NY…

A: Given, for males born in upstate NY, the gestation times are normally distributed with a mean of 39…

Q: The scores on a mathematics exam have a mean of 71and a standard deviation of 8. Find the x-value…

A: Let X denote the scores on a mathematics exam and it follows normal distribution with mean of…

Q: find the 80th percentile of a normal distribution where x=n(50,10)

A: Step 1:Find the 80th percentile of a normal distribution.X∼N(50,10)=X∼N(μ,σ)Step 2:Find the Z-score…

Q: Use the normal distribution of IQ scores, which has a mean of 130 and a standard deviation of 15,…

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: The center of a normal curve is the mean of the distribution. O is the standard deviation. O cannot…

A: Answer  The center of a normal curve is the mean of the distribution. It is a bell-shaped curve.…

Q: Assume that the data has a normal distribution and the number of observation is greater than fifty.…

A: Significance level (alpha) = 0.09 We know that,  If x is random variable from standard normal…

Q: A normal distribution has a mean of 130 and a standard deviation of 4. Fing the z-score for a data…

A: The mean is 130 and the standard deviation is 4.

Q: The useful life of a bicycle bought at Basement-mart fits a log normal distribution with a mean of…

A: Mean ()=16Standard deviation ()=10.36Sample size(n)=60

Q: Find the probability that z is between two value 0.43 and 0.72 . Sketch the normal curve/s neatly

A: As per given by question, find the probability that z is between value 0.43 and 0.72. Now, For…

Q: Assume that people playing World of Warcraft in a week has a normal distribution with a mean of 54…

A: This question requires us to use the normal distribution to calculate the probability of a randomly…

Q: Assume that x has a normal distribution with mean =4 and standard deviation q=2. Find (3<x<6)

A: Given   x has a normal distribution  mean μ=4  standard deviation σ=2 Find p(3&lt;x&lt;6)=?

Q: derive the variance of standard normal distribution using the MGF; show complete solution.

A: Given: random variable x follow standard normal distribution then derive the variance of standard…

Q: A normal distribution has a mean of 125 and a standard deviation of 3. Find the z-score for a data…

A: A normal distribution has a mean of 125 and a standard deviation of 3. mu

Q: Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(–…

A: Given X is normally distributed X ~ N(0,1)

Q: Use R to determine P(3.1<ỹ<5.1) for a Normal distribution with a mean of 4.3 and a standard…

A: Use R programming

Q: Identify if its true or false A normal distribution is symmetrical at the mean, i.e. the left side…

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Q: Find the probability that a standard normal variable takes on a value between -1.59 and 3.0. Also…

A:

Q: Assume a normal distribution. What is p(z > +1 .75)?

A: Z follows standard normal distribution with mean 0 and variance 1

Q: A standard normal distribution has a mean of one and a standard deviation of three. True False

A: The standard normal distribution is a normal distribution with a mean of zero and standard deviation…

Q: X is the time of completing a task using a specific tool. X has a normal distribution with a mean of…

A: Given data,Mean μ=25variance σ2=49Standard deviation σ=7z-score=-3.72x=?

Q: Find area to the right of 2 for standard normal distribution.b

A: we have to find right of 2.......for standard normal distribution...

Q: X is the time of completing a task using specific software. X has a normal distribution with a mean…

A: X has normal distribution with mean µ = 24 and variance, σ 2 = 49 =&gt; standard deviation σ = 7 We…

Q: Let the random variable X follow a normal distribution with a mean of 18 and a standard deviation of…

A:

Q: Select all the properties that must be true of a normal distribution.

A: We give the correct option and some explanation is discuss.  Normal distribution graph

Q: Describe the difference in shape between a gamma(shape = 5, rate= 10) distribution and a beta(shape…

A: Given:- γα=5,λ=10    and    βa=10,b=5   we have to find mean,skew and interquartile range

Q: Find the Z score for which 80% of the distributions area lies between -z and z

A: Solution: From the given information, the area lies between –z and z is 0.80.

Q: Find -z and z such that 55% of the standard normal curve lies between –z and z.

A: Given data  55% of area of standard normal curve lies between -Z and Z.  we have to find value of -z…

Q: Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and…

A: Z has standard normal distribution. where mean=0 and standard deviation=1 i.e. Z~N0,1

Q: Prob-6 To avoid any high-speed imbalance in a rotating shaft; it needs to have a variance of its…

A: Given: Hypothesized variance σ2=0.0004 Sample size (n) = 16 Sample standard deviation (s) = 0.018…

Q: Scores on a particular test, taken by a large group of students, follow a normal distribution with a…

A:

Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard…

A:

Q: Determine the appropriate z or t alpha value and calculate the error bound for the mean.

A: From the previous calculation we have  Sample size (n) = 40Sample mean (x̅) = 233067.5Standard…

Q: International Journal of Statistical Distributions (Vol. 1, 2015) study of a variable life insurance…

A: Solution:  let X be the rates of return of the  investment for two consecutive year has normal…