Question

Given a random variable XX following normal distribution with mean of -3 and standard deviation of 4. Then random variable Y=0.4X+5Y=0.4X+5 is also normal.

(1)(2pts) Find the distribution of YY, i.e. μY,σY.μY,σY.

(2)(3pts) Find the probabilities P(−4<X<0),P(−1<Y<0).P(−4<X<0),P(−1<Y<0).

(3)(3pts) Find the probabilities P(−4<X¯<0),P(3<Y¯<4).P(−4<X¯<0),P(3<Y¯<4).

(4)(4pts) Find the 53th percentile of the distribution of XX.

Answer #1

Given a random variable X following normal distribution with
mean of -3 and standard deviation of 4. Then random variable
Y=0.4X+5 is also normal.
(1)Find the distribution of Y, i.e. μy,σy
(2)Find the probabilities P(−4<X<0),P(−1<Y<0)
(3)Find the probabilities(let n size =8)
P(−4<X¯<0),P(3<Y¯<4)
(4)Find the 53th percentile of the distribution of X

Let X and Y have a bivariate normal distribution with parameters
μX = 0, σX = 3; μY = 8,
σY = 5; ρ = 0.6. Find the following probabilities.
P(-6 < X < 6)
P(6 < Y < 14 | X = 2)

Given that x is a Normal random variable with a mean of 10 and
standard deviation of 4, find the following probabilities:
P(x<7.6)
P(x>11.5)
P(8.9<x<13.5)
Given that x is a Normal random variable with a mean of 10 and
standard deviation of 4, find x for each situation:
the area to the left of x is 0.1
the area to the left of x is 0.75
the area to the right of x is 0.35
the area to the right...

Let X and Y have a bivariate normal distribution with parameters
μX = 0, σX = 3; μY = 8, σY = 5; ρ = 0.6. Find the following
probabilities.
(A) P(-6 < X < 6)
(B) P(6 < Y < 14 | X = 2)

Assume a normal random variable, X, with mean 90 and standard
deviation 10. Find the probability that a randomly chosen value of
X is less than 95. Find the probability that a randomly chosen
value of X is between 60 and 100. Find the 97th percentile of the X
distribution (i.e., find the value x such that P(X<x)=0.97).
Find the probability that a randomly chosen value of X is greater
than 100, given that it is greater than 90 (i.e.,...

1. If the random variable Z has a standard normal
distribution, then P(1.17 ≤ Z ≤ 2.26) is
A) 0.1091
B) 0.1203
C) 0.2118
D) 0.3944
2. Choose from the Following: Gaussian Distribution, Empirical
Rule, Standard Normal, Random Variable, Inverse Normal, Normal
Distribution, Approximation, Standardized, Left Skewed, or
Z-Score.
The [_______] is also referred to as
the standard normal deviate or just the normal deviate.
3. The demand for a new product is
estimated to be normally distributed with μ...

If X is a normal
random variable with a mean of 78 and a standard deviation of 5,
find the following probabilities:
a) P(X ≥ 78)
(1 Mark)
b) P(X ≥ 87)
(1 Mark)
c) P(X ≤ 91)
(1 Mark)
d) P(70
≤ X ≤ 77)
(1 Mark)

Let X be a random variable with the following probability
distribution: Value x of X P=Xx 1 0.15 2 0.55 3 0.05 4 0.15 5 0.10
Find the expectation EX and variance Var X of X .

Suppose X has a normal distribution with mean 3 and standard
deviation 1. The 95th percentile of this distribution is
Group of answer choices
4.28
-4.28
4.94
-4.64
4.64
2.
Suppose X = 5 is a measurement from a normal population with
mean 2 and standard deviation 3. The corresponding Z-score is
Group of answer choices
2
5
0
1
3
3. Suppose X is a standard normal random variable. Among other
things this implies that the mean of X...

A random variable X follows a normal distribution with
mean 135 and standard deviation 12. If a sample of size 10 is
taken, find P (x̅ < 137). (4 decimal places) Find the answer
using StatCrunch.

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