Question

what is the mean value and the standard deviation of the standardized random variable z used in statistics ?

Answer #1

For the standardized random variable z has a mean equal to 0 and standard deviation equal to 1.

If any normal variable X has a mean and standard deviation then standardized random variable z is:

This is formula for z.

The main answer is: **mean = 0, standard deviation =
1** for standardized random variable.

Please comment if any doubt. Thank you.

Let z be a normal random variable with mean 0 and
standard deviation 1. What is
P(-2.25 < z < -1.1)?
a 0.3643
b 0.8643
c 0.1235
d 0.4878
e 0.5000
Let zbe a normal random variable with mean 0 and
standard deviation 1. The 50thpercentile of zis
____________.
a 0.6700
b -1.254
c 0.0000
d 1.2800
e 0.5000
Let zbe a normal random variable with mean 0 and
standard deviation 1. The 75thpercentile of zis
____________.
a 0.6700
b...

A continuous random
variable Z follows standard normal distribution.
a) What is the mean of
Z?
b) What is the
standard deviation of Z?
c) Z=(x-10)/5 What is
the distribution of X ?

given normal random variable Z with mean μ= 57.1 and standard
deviation σ=13.2, what is P (Z > 46)?

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...

1.Suppose X is a random variable that is normally distributed with mean 5 and standard deviation 0.4. If P (X≤X0) = P (Z≤1.3). What is the value of X0.?
Select one:
2.00
5.52
6.90
4.48
2.Suppose X is a random variable that is normally distributed with a mean of 5. If P (X≤3) = 0.2005, what is the value of the standard deviation?
Select one:
σ = 2.38
σ = −2
σ = 1.38
σ = 2

In each situation below, calculate the standardized score (or
z-score) for the value x.
(a) Mean μ = 0, standard deviation σ = 1, value x = 1.7. z =
(b) Mean μ = 9, standard deviation σ = 4, value x = 5. z =
(c) Mean μ = 14, standard deviation σ = 7, value x = 0. z =
(d) Mean μ = -15, standard deviation σ = 15, value x = -60. z
=

Given a standardized normal
distribution (with a mean of 0 and a standard deviation of 1) what
is the probability that
Z is between -1.23 and 1.64
Z Is less than -1.27 or greater than 1.74
For normal data with values symmetrically distributed around
the mean find the z values that contain 95% of the data
Find the value of z such that area to the right is 2.5% of the
total area under the normal curve

Given a standardized normal distribution (with a mean of 0 and a
standard deviation of 1) what is the probability that: Z is less
than 1.08?, Z is greater than -0.21?, Z is less than -0.21 or
greater than the mean, Z is less than -0.21 or greater than
1.08?

Given a standardized normal distribution (with a mean of 0 and
a standard deviation of 1)
(round to 4 decimal places)
a) What is the probability that Z is between −1.59 and 1.88?
b) What is the probability that Z is less than −1.59 or greater
than 1.88?
c) What is the value of Z if only 1% of all possible Z values
are larger?
d) Between what two values of Z (symmetrically distributed
around the mean) will 98.36% of...

2.)Assume random variable Z follows standard normal
distribution; find the value of the following probabilities.
P(-1<Z<1)
3.)Assume random variable Z follows standard normal
distribution; find the value of the following probabilities.
P(0<Z<1)
4.)Assume random variable Z follows standard normal
distribution; find the value of the following probabilities.
P(Z>2)
5.)The natural log of growth of yucca tree is approximately
normally distributed with mean of 0.053 mm and standard deviation
0.03mm. Determine the probability that a yucca tree has growth less
than...

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