Question

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

Answer #1

**Answer:**

Given Data

A random variable X following normal distribution

Mean = -3

Standard deviation = 4

Random variable Y=0.4X+5 is also normal distribution

1)Find the distribution of Y, i.e. μy,σy

= -1.2 + 5

= 3.8

= 2.56

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

P(−1<Y<0)

=

= I(-2.375)-I(2.375)

= I(3) - I(2.375)

= 0.998 - 0.991

= 0.007

3)Find the probabilities(let n size =8)

=

=

4)Find the 53th percentile of the distribution of X

2.68

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...

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.

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)

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 has a Normal distribution with an unknown
mean and a standard deviation of 12. Suppose that we take a random
sample of size ?=36n=36 and find a sample mean of ?¯=98x¯=98 . What
is a 95% confidence interval for the mean of ?x ?
(96.355,99.645)(96.355,99.645)
(97.347,98.653)(97.347,98.653)
(94.08,101.92)(94.08,101.92)
(74.48,121.52)

given normal random variable x with mean μ= 57.1 and standard
deviation σ=13.2, what is P (46 < x̄ < 69)
for a sample of size n= 16?

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)

The random variable x has a normal distribution with mean 23 and
standard deviation 5.
Find the value d such that P(20<X<d)=0.4641

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)

Find the mean, variance, and standard deviation of the random
variable having the probability distribution given in the following
table. (Round your answers to four decimal places.)
Random variable, x
-7
-6
-5
-4
-3
P(X = x)
0.13
0.16
0.4
0.15
0.16

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 12 minutes ago

asked 12 minutes ago

asked 17 minutes ago

asked 20 minutes ago

asked 22 minutes ago

asked 24 minutes ago

asked 25 minutes ago

asked 32 minutes ago

asked 32 minutes ago

asked 32 minutes ago

asked 34 minutes ago