Question

The Normal Probability Distribution In §6.2 we are introduced to the Normal Probability Distribution and the special case of the Normal Probability Distribution, the Standard Normal Probability Distribution, which is a Normal Probability Distribution with mean (u) zero and variance (σ2) one (and standard deviation of

1). What is a z score?

2. What is the purpose of a z score?

3. If a z score were -3, where on the graph would it be? Is this a rare or a common score? Why? One way to find probabilities from a Standard Normal Distribution is to use probability tables, which are located inside the front cover of your textbook.

4. According to the table, what is the probability when z ≤ -1.23? The probability when z ≤ 1.23? 5. Select two other pairs of "opposites" on the z table (like 2, -2 etc.) and give their probabilities. 6. Show the math of adding each of the pairs. What is the total each time? Why is that the total? 7. What are the properties of the Standard Normal Probability Distribution?

Answer #1

Dear student, we can provide you with a solution of 4 subquestions at a time.

1) A **z**-**score** is the number of
standard deviations from the mean a data point is. It's a measure
of how many standard deviations below or above the population mean
a raw score is.

2) The standard score is a very useful statistic because it allows us to calculate the probability of a score occurring within our normal distribution and it enables us to compare two scores that are from different normal distributions.

3)

This is a rare score, as the score corresponding to this is 3 standard deviations below the mean.

4)

This week we study Normal Distribution. First, see all material
posted on Blackboard in section: Course Material - week 9. Also
read sections 6.1, 6.2, 6.3 in Chapter 6 of the eText. Then, post
your submission for Part 1 and Part 2 below. Part 1. Demonstrate
that you understand basic concept of Normal Distribution. In two
small paragraphs describe a couple of properties/rules of Normal
distribution. Hint: look for KEY FACTS and DEFINITIONS in sections
6.1 and 6.2 of eText....

Table 1: Cumulative distribution function of the standard Normal
distribution
z: 0 1 2 3 Probability to the left of z: .5000 .84134 .97725 .99865
Probability to the right of z: .5000 .15866 .02275 .00135
Probability between z and z: .6827 .9544 .99730
Table 2: Inverse of the cumulative distribution function of the
standard Normal distribution
Probability to the left of z: . 5000 .92 .95 .975 .9990 z: 0.00
1.405 1.645 1.960 3.09
1 Normal Distributions
1. What proportion...

NOTE: Since we are given the Standard Normal
Distribution, we are able to go directly to Table V to find the
requested probabilities.
What is the area under the curve such that z is less
than - 2.20 ?
What is the area under the curve such that z > - 2.20
?
What is the probability that z is less than 7.03
?
What is the probability that z is greater than 7.03
?

Use the standard normal (z score) table to find: P(-1.00 ≤
z)
Find the probability that a data value picked at random from a
normal population will have a standard score (z) that lies between
the following pairs of z-values. z = 0 to z = 2.10

This week we study Normal Distribution.
Part 1. Demonstrate that you understand basic concept of Normal
Distribution.
In two small paragraphs describe a couple of properties/rules of
Normal distribution.
Give one example of some practical case where we can use Normal
distribution (for instance, IQ scores follow a normal distribution
of probabilities with the mean IQ of 100 and a standard deviation
around the mean of about 15 IQ points.)
Part 2. Assign your numbers for mean μ and standard...

Q1-. A normal distribution has a mean of 15 and a standard
deviation of 2. Find the value that corresponds to the 75th
percentile. Round your answer to two decimal places.
Q2-.Tyrell's SAT math score was in the 64th percentile. If all
SAT math scores are normally distributed with a mean of 500 and a
standard deviation of 100, what is Tyrell's math score? Round your
answer to the nearest whole number.
Q3-.Find the z-score that cuts off an area...

Q1-. A normal distribution has a mean of 15 and a standard
deviation of 2. Find the value that corresponds to the 75th
percentile. Round your answer to two decimal places.
Q2-.Tyrell's SAT math score was in the 64th percentile. If all
SAT math scores are normally distributed with a mean of 500 and a
standard deviation of 100, what is Tyrell's math score? Round your
answer to the nearest whole number.
Q3-.Find the z-score that cuts off an area...

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

The average apartment rental at Gotham is approximately $615 per
month. Suppose these rates are roughly normal with a standard
deviation of $100. What proportion of rentals:
1. is at least $710 per
month?
2. is less than $450 per
month?
3. is between $450 and $800 per
month?
Use the Z-score table of Areas Under the Standardized Normal
Distribution. You may find it in Appendix D of the Basic
Econometrics textbook.
Please round your Z score to the nearest...

This week, we are
studying a type of continuous probability distribution that is
called a normal distribution. One real-life example of a normal
distribution is IQ score. The mean of this distribution is 100 with
a standard deviation of 15.
For this week's
discussion, do a little research and share another real
life example of a normal distribution, including information about
the mean and standard deviation. Post a diagram to share
with the class.

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