Question

- 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 of x is 0.95

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

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.

A normal random variable x has an unknown mean and standard
deviation. The probability that x exceeds 4 is 0.975, and the
probability that x exceeds 5 is 0.95. Find μ and σ.

Given that x is a normal variable with mean ? = 114 and standard
deviation ? = 12, find the following probabilities. (Round your
answers to four decimal places.) (a) P(x ? 120) (b) P(x ? 80) (c)
P(108 ? x ? 117)

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)

Given that x is a normal variable with mean μ = 108 and standard
deviation σ = 14, find the following probabilities.
(a) P(x ≤ 120)
(b) P(x ≥ 80)
(c) P(108 ≤ x ≤ 117)

If X is a normal variable with mean 85 and standard deviation
10, find P left parenthesis 65 less or equal than X less or equal
than 100 right parenthesis. Round to four decimal places.

Given that x is a normal variable with mean μ
= 51 and standard deviation σ = 6.5, find the following
probabilities. (Round your answers to four decimal places.)
(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)

Given that x is a normal variable with mean μ
= 48 and standard deviation σ = 6.2, find the following
probabilities. (Round your answers to four decimal places.)
(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)

Given that x is a normal variable with mean μ = 111 and standard
deviation σ = 14, find the following probabilities. (Round your
answers to four decimal places.) (a) P(x ≤ 120) (b) P(x ≥ 80) (c)
P(108 ≤ x ≤ 117)

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