Find the following probabilities for the standard normal random variable z: (a) P(-1.08 < z< 0.5) = (b) P(-0.87 < z < 1.54) = (c) P(z< 1.42) = (d) P(z> –0.4) =

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A: X P(X) 6 0.1 0.6 36 3.6 8 0.13 1.04 64 8.32 10 0.14 1.4 100 14 12 0.08 0.96 144 11.52…

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A:

Q: 5)- Let y1, Y2, ..., Yn be a random sample of n observations from a normal distribution with mean O…

A: Given: Y1, ............Yn ~ N (0, σ2) fy=12πσ2×e-12×y2σ2          y≥0

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A: Given that: P (-2.21 &lt; Z &lt; -1.39)

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Q: Since P {x=-1} = P {x=1} = 1/2 , calculate the expected value and variance of the X random variable.…

A: Solution: From the given information,

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…

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A:

Q: If Z is a random variable from a standard normal distribution and if P(Z < a) = 0.72, then %3D P(Z <…

A: Therefore,

Q: Given that Z is a standard normal random variable, P(-1≤Z≤1.5) is?

A: Using the excel following standard normal probabilities can be obtained as:

Q: Find E[Z] and Var (Z) where Z is standard normal random variable with parameters H and

A: We know that the  Standard Normal distribution has a mean 0 and standard deviation of 1.

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A:

Q: Let X be a random variable with the following probability distribution: -3 6 9 f(x) | 1/6 1/2 1/3…

A: GivenLet X be a random variable x -3 6 9 f(x) 16 12 13

Q: Consider the discrete random variable x given in the table below. Calculate the mean, variance, and…

A:

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Q: Let z be a normal random variable with mean 0 and standard deviation 1. The 50th percentile of z is…

A: Given that, Z be a normal random variable with mean 0 and standard deviation 1.

Q: B. Find the probabilities on a standard normal curve. 1. P( z>-1.32) 2. P( z< 0.45)

A: The probabilities on a standard normal curve are calculated as: 1.…

Q: If E denotes the expectation the variance of a random variable X is denoted as

A: Here use mean and Variance of random variable X

Q: Consider the discrete random variable X given in the table below. Calculate the mean, variance, and…

A: Note: Thank you for the question. Since multiple questions are posted, according to our policy, we…

Q: Consider the discrete random variable X given in the table below. Calculate the mean, standard…

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Q: Let X be a discrete random variable with Poisson distribution, and with a standard deviation of 6.5.…

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Q: P(x) 0.645 1. 0.297 0.052 0.005 0.001 0.000 2345

A: We have to use following formulae , Standard deviation : σ = ∑( x - μ)2p(x) Where , μ is mean μ =…

Q: A discrete random variable X has the following probability distribution: -4 -3 -2 -1 2 3 0.05 0.075…

A:

Q: Suppose the random variable Z follows a standard normal distribution. Then the value of P(-2.21 <…

A: The Random variable Z follows a standard normal distribution We need to calculate

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A: Consider the table:

Q: If Z is a random variable from a standard normal distribution and if P(Z> c) = 0.22, then P(Z < -C)…

A: Z is a random variable from a standard normal distribution.

Q: For a standard normal random variable Z, P(-0.86<Z<-0.24) =?

A:

Q: Let X be a random variable with an expected value of 0, and let X² have an expected value of 9. Find…

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Q: Let X be a random variable with P(X = 1) = 0.2, P(X = 2) = 0.3, and P(X = 3) = 0.5. What is the…

A: Given information: The random variable X has the following probability distribution: X P(X=x) 1…

Q: x 0 1 2 3 4 P(X=x) 0.1 0.25 k 0.30 0.20 Based on the table above, answer the following questions: a)…

A: a) Suppose a random variable x has probability distribution of p(x), which is said to be a valid…

Q: 1. n = 30 and p = 0-6 2. n = 50 and p = 0.45 3. n = 80 andp= 0.35

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: Consider the discrete random variable XX given in the table below. Calculate the mean, variance, and…

A: Given data, X P(X) X*P(X) X^2*P(X) 2 0.56 1.12 2.24 5 0.08 0.4 2 8 0.08 0.64 5.12 9 0.14…

Q: Find the following probabilities for the standard normal random variable z (1 point) Find the…

A: We have given that the standard normal random variable z  Note: According to Bartleby expert…

Q: Find the following probabilities for the standard normal random variable z:   (a) P(-0.87 \leq z…

A:

Q: The number of ships to arrive at a harbour on any given day is a random variable represented by X.…

A: The expected value can be calculated as: Therefore, the expected value is 9.320

Q: A) For a standard normal distribution, the probability of z 0 is B) Given that Z is a standard…

A: Note: Hey there! Thank you for posting the question. For calculating probability, we are considering…

Q: 1. Let Z be a standard normal random variable. Calculate the following probabilities.

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

Q: x f(x) 20 0.10 25 0.20 30 0.25 35 0.15 40 0.10 a. What is the probability that the firm will obtain…

A: Given data is x f(x) 20 0.10 25 0.20 30 0.25 35 0.15 40 0.10

Q: Let Z be the standard normal random variable Find P (Z > -0.72)

A: Given that  X~N(0,1) be a standard normal distribution To find P(Z&gt;-0.72)=?…

Q: The probability distribution of random variable X is defined as follows:   X 0 1 2 3 4…

A: mean=expected value=E(X)=∑xP(X)

Q: Find the following probabilities for the standard normal random variable z (Keep in mind that the…

A: Using the standard normal distribution we get:1)  P(z&lt;1.99)=0.9767

Q: X is a discrete random variable with the following PMF: P(X = -9.2) = 0.25 P(X = -2.5) = 0.25 P(X =…

A:

Q: The following table lists the probability distribution of a discrete random variable x: x 2 3 5 6 4…

A: Given problem Given that   The following table lists the probability distribution of a discrete…

Q: Consider the discrete random variable X given in the table below. Calculate the mean, variance, and…

A: The mean of the random variable X is given by:…

Q: Assume Z is a standard normal random variable.

A: We have to assume Z is a standard normal random variable it means Z~ N(0,1) Where Z=X-μσ~N(0,1)

Q: Compute the mean and standard deviation of the random variable with the given discrete probability…

A: Ans - Given table     x P(x) x*P(x) x2P(x) -6 0.25 -1.5 9.0 -5 0.11 -0.55 2.75 6 0.23 1.38…

Q: Consider the standard normal random variable Z. What is PZ> -0.32)?

A: Is is given that Z is standard normal variable i.e Z follows N(mean = 0, SD = 1).