Question

The Standard Normal Distribution with a mean of 0 and a standard
deviation of 1 has been used to calculate areas under the normal
distribution curve. Originally, quality control analysts were
content to confine all data within +/- **three**
standard deviations from the mean. The Ford Motor Company in the
mid 1980s decided to try to confine all data within +/-
**four** standard deviations from the mean. Six Sigma,
the newest quality venture, is trying to confine all data within
+/- **six** standard deviations from the mean. If the
distance between the mean and the **three**,
**four**, and **six** sigma limits is the
same for all three, what must be happening to the value of the
standard deviation and what impact might that have in the control
of quality and the production of usable outputs? (Hint: you might
want to check Z values for +/- 3, 4, 6 and see what is happening to
the probabilities of values beyond these limits.)

Response due by Thursday 11:59pm; [up to 10 points] In eight to ten well-constructed sentences, respond to DQ 3. Be sure to use proper grammar, as well as correct spelling and punctuation.

Answer #1

The mean of this data is 3.65217391 and the standard deviation
is 2.30839742
The questions:
1. Compare the first value of your data (8) to the mean
(3.6521..)
* Is this value within ONE standard deviation of the mean? Is it
beyond one standard deviation of the mean? Is it more than two
standard deviations from the mean but within three?
* Are there any values that are more than three standard
deviations from the mean? (Identify the limits of...

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

A data set has a mean of 135, a median of 137, and a standard
deviation of 13. Marrion concludes that 99.7% of the data in the
set must have values between 96 and 174.
What flaw, if any, is there in Marrion’s reasoning? Pick only
one.
A. Marrion should have calculated three standard deviations from
the median instead of calculating three standard deviations from
the mean.
B. There is no flaw in Marrion’s reasoning. He calculated three
standard deviations...

For a normal distribution, find the percentage of data that are
(a) Within 1 standard deviation of the mean __________ % (b)
Between ?−3.5? μ − 3.5 σ and ?+2.5? μ + 2.5 σ ____________% (c)
More than 2 standard deviations away from the mean _________%

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...

Suppose x has a normal distribution with mean μ = 16 and
standard deviation σ = 11. Describe the distribution of x values
for sample size n = 4. (Round σx to two decimal places.)
μx = σx = Describe the distribution of x values for sample size
n = 16. (Round σx to two decimal places.)
μx = σx = Describe the distribution of x values for sample size
n = 100. (Round σx to two decimal places.)
μx...

Suppose x has a normal distribution with mean μ = 26 and
standard deviation σ = 6. Describe the distribution of x values for
sample size n = 4. (Round σx to two decimal places.) μx = σx =
Describe the distribution of x values for sample size n = 16.
(Round σx to two decimal places.) μx = σx = Describe the
distribution of x values for sample size n = 100. (Round σx to two
decimal places.) μx...

Suppose x has a normal distribution with mean
μ = 31 and standard deviation σ = 11.
Describe the distribution of x values for sample size
n = 4. (Round σx to two
decimal places.)
μx
=
σx
=
Describe the distribution of x values for sample size
n = 16. (Round σx to two
decimal places.)
μx
=
σx
=
Describe the distribution of x values for sample size
n = 100. (Round σx to two
decimal places.)
μx...

Suppose x has a normal distribution with mean μ = 52 and
standard deviation σ = 4. Describe the distribution of x values for
sample size n = 4. (Round σx to two decimal places.) μx = σx =
Describe the distribution of x values for sample size n = 16.
(Round σx to two decimal places.) μx = σx = Describe the
distribution of x values for sample size n = 100. (Round σx to two
decimal places.) μx...

Suppose x has a normal distribution with mean
μ = 57 and standard deviation σ = 7.
Describe the distribution of x values for sample size
n = 4. (Round σx to two
decimal places.)
μx
σx
Describe the distribution of x values for sample size
n = 16. (Round σx to two
decimal places.)
μx
σx
Describe the distribution of x values for sample size
n = 100. (Round σx to two
decimal places.)
μx
σx
How do the...

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