Question

The entity X ~ N(0, 1) (Standard normal distribution). (a) Find q such that Pr(X <= q) = 0.25 (the first quartile of the standard normal distribution); (b) Find q such that Pr(X <= q) = 0.75 (third quartile of the standard normal distribution)

Answer #1

The first quartile is at -0.67 and the third quartile is at 0.67. U can refer standard normal table for the answer.

For more precise answer one can use percentile calculator of normal distribution.

Using calculator, the first quartile is at -0.6745 and third quartile is at 0.6745.

The entity X ~ N(4, 2). Calculate (a) Pr(X ≤ 3.7); (b) Pr(X ≥
5.2); and (c) Pr(3.7 < X < 5.2).

If X has a normal distribution M=5 and Standard deviation = 2
find Pr(2< X < 6)

Problem 6.
1. If X ~ N(9; 4), find Pr(|X - 2 |< 4).
2. If X ~ N(0; 1), find Pr(|X + 3|> 5).
3. If X ~ N(-2; 9), find the number c such that Pr(|X + 2| < c)
= 0:5.

Prove that Pr[A] ≤ min(1, q/p) when Pr[B|A] ≥ p > 0 and Pr[B]
≤ q

1. Suppose X~N(0,1), what is Pr (0<X<1.20)
2. Suppose X~N(0,1), what is Pr (0<X<1.96)
3. Suppose X~N(0,1), what is Pr (X<1.96)
4. Suppose X~N(0,1), what is Pr (X> 1.20)
Please use step by step work. I'm struggling with grasping the
process. Thank you.

1. What is the first quartile of a normal distribution
with mean 40, and standard deviation 7? Round to three decimal
places.
2. What is the third quartile of a normal distribution
with mean 40, and standard deviation 7? Round to three decimal
places.
3. What is the IQR of a normal distribution with mean
40, and standard deviation 7? Round to three decimal
places.

) Suppose a random sample Y1, ..., Y100 are from the standard
normal population N(0, 1).
(a) Write down the distribution of Y¯
(b) calc the probability Pr(Y¯ < 0.1)
(b) Calculate the probability Pr(Y¯ > a) = 0.9.
*the bar beside the Ys are supposed to be above them

Example 1: Suppose X ∼ N (0, 1), that is, X is a standard normal
random variable. Let Y = X2. Find the pdf of Y ,
fy(y).

If a random variable X follows a standard normal model N(0, 1),
find the
density of X^2
For two independent standard normal random variables X and Y,
find
the density of X^2+Y^2
For three independent standard normal random variables X, Y and
Z,
find the density of X^2+Y^2+Z^2
If a random variable X follows a normal N(μ,σ^2), and a
random variable
Y follows a χ2 (Chi-Square) model with degree of freedom k, assume that X
and Y are
independent,
4.1)...

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

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