Question

Suppose X is a random variable with with expected value -0.01
and standard deviation *σ* = 0.04.

Let

*X*_{1},
*X*_{2}, ...
,*X*_{81}

be a random sample of 81 observations from the distribution of
X.

Let *X* be the sample mean. Use R to determine the
following:

Copy your R script

b) What is the approximate probability that

*X*_{1} +
*X*_{2} + ...
+*X*_{81} >−0.02?

Answer #1

Suppose X is a Normal random variable with with expected value
31 and standard deviation 3.11. We take a random sample of size n
from the distribution of X. Let X be the sample mean. Use R
to determine the following:
a) What is the standard deviation of X when n =
19?
b) What is the probability that X1 + X2 +
... +X20 > 630?
PLEASE ANSWER IN R SCRIPT

Question 7) Suppose X is a Normal random variable with with
expected value 31 and standard deviation 3.11. We take a random
sample of size n from the distribution of X. Let X be the sample
mean. Use R to determine the following:
a) Find the probability P(X>32.1):
b) Find the probability P(X >32.1) when n = 4:
c) Find the probability P(X >32.1) when n = 25:
d) What is the probability P(31.8 <X <32.5) when n =
25?...

Let the random variable X follow a distribution with a mean of
μ and a standard deviation of σ. Let X1 be the mean of a sample of
n1 (n1=1) observations randomly chosen from
this population, and X2 be the mean of a sample of n2(
n2 =49) observations randomly chosen from the same
population. Which of the following statement is False? Evaluate the
following statement.
P(μ
- 0.2σ <X 1 < μ + 0.2σ) <
P(μ - 0.2σ <X...

A random variable x has the following probability distribution.
Determine the standard deviation of x.
x
f(x)
0
0.05
1
0.1
2
0.3
3
0.2
4
0.35
A random variable x has the following probability distribution.
Determine the expected value of x.
x
f(x)
0
0.11
1
0.04
2
0.3
3
0.2
4
0.35
QUESTION 2
A random variable x has the following probability distribution.
Determine the variance of x.
x
f(x)
0
0.02
1
0.13
2
0.3
3
0.2...

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...

Using the formulas for the mean and standard deviation of a
discrete random variable, calculate to 2 decimal places the mean
and standard deviation for the population probability distribution
of the table below.
x
P(x)
69
0.20
79
0.22
81
0.35
98
0.23
μ =
σ =

If x represents a random variable with mean 147 and standard
deviation 45, then the standard deviation of the sampling
distribution of the means with sample size 81 is 5.
True
False

Suppose X is a random variable with expected value 260 and
standard deviation 120, and Y is a random variable with expected
value 170 and standard deviation 70. Compute each of the means and
standard deviations indicated below (round off your answers to two
decimal places, if necessary).
E(1.7X)=
SD(1.7X)=
SD(X+Y)=
E(X−Y)=
SD(X−Y)=
Now let Y1 and Y2 be two instances of the random variable YY and
compute the following (again, rounding to two decimal places, if
necessary).
E(Y1+Y2)=
SD(Y1+Y2)=...

Let X1, X2,...,Xn represent n random draws from a population
with standard deviation σ and variance σ^2 , so that V ar[X1] = V
ar[X2] = ... = V ar[Xn] = σ^ 2 . Define the sample average taken
from a sample of size n as follows: X¯ n ≡ (X1 + X2 + ... + Xn)/ n
.
a) Derive an expression for the standard deviation of X¯ n.
[Hint: Your answer should depend only on σ and n]...

Answer the question for a normal random variable x with
mean μ and standard deviation σ specified below.
(Round your answer to one decimal place.)
μ = 38 and σ = 8.
Find a value of x that has area 0.01 to its right.

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