Question

The mean and standard deviation of a random variable x are 7 and 4 respectively. Find the mean and standard deviation of the given random variables:

(1) y=x+1 μ= σ=

(2) v=8x μ= σ=

(3) w=8x+1 μ= σ=

Answer #1

The mean and standard deviation of a random variable x are 10
and 3 respectively. Find the mean and standard deviation of the
given random variables:
(1) y=x+4
μ=
σ=
(2) v=9x
μ=
σ=
(3) w=9x+4
μ=
σ=

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.

Find the mean, μ, and standard deviation, σ, for a binomial
random variable X. (Round all answers for σ to three decimal
places.)
(a) n = 45, p = .50.
μ =
σ =
(b) n = 1, p = 0.25.
μ =
σ =
(c) n = 100, p = 0.75.
μ =
σ =
(d) n = 30, p = .01.
μ =
σ =

X is a normal random variable with mean μ and standard
deviation σ. Then P( μ− 1.2 σ ≤ X ≤ μ+ 1.9 σ) =?
Answer to 4 decimal places.

7. A normal random variable x has mean μ = 1.7
and standard deviation σ = 0.17. Find the probabilities of
these X-values. (Round your answers to four decimal
places.)
(a) 1.00 < X <
1.60
(b) X > 1.39
(c) 1.25 < X < 1.50
8. Suppose the numbers of a particular type of bacteria in
samples of 1 millilitre (mL) of drinking water tend to be
approximately normally distributed, with a mean of 81 and a
standard deviation of 8. What...

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

i) A random variable X has a binomial distribution with mean 6
and variance 3.6: Find P(X = 4).
ii) Let X equal the larger outcome when a pair of four-sided
dice is rolled. The pmf of X is
f(x) = (2x - 1/ 16) ; x = 1; 2; 3; 4.
Find the mean, variance and standard deviation of X.
iii) Let μ and σ^2 denote the mean and variance of the random
variable able X. Determine E [(X...

Suppose X is a normal random variable with mean
μ = 100 and standard deviation σ = 7. Find
b such that
P(100 ≤ X ≤
b) = 0.3.
HINT [See Example 3.] (Round your answer to one decimal
place.)
b =

If x is a binomial random variable, compute the mean,
the standard deviation, and the variance for each of the following
cases:
(a)
n=4,p=0.7
μ=
σ2=
σ=
(b)
n=3,p=0.7
μ=
σ2=
σ=
(c)
n=5,p=0.4
μ=
σ2=
σ=
(d)
n=5,p=0.8
μ=
σ2=
σ=

Suppose that X is a random variable with mean 21 and standard
deviation 4 . Also suppose that Y is a random variable with mean 42
and standard deviation 8 . Find the mean of the random variable Z
for each of the following cases
(Give your answer to three decimal places.)
a) Z = 3 + 10X
b) Z = 3X − 10
c) Z = X + Y
d) Z = X − Y
e) Z = −4X...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 8 minutes ago

asked 8 minutes ago

asked 26 minutes ago

asked 26 minutes ago

asked 40 minutes ago

asked 41 minutes ago

asked 44 minutes ago

asked 55 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 1 hour ago