Chat with us, powered by LiveChat Review course text and Moodle notes on the Normal Distribution Review this article on the Normal Distribution applied to business salary problems https://www.wallstreetmojo.com/normal- EssayAbode

25 Apr Review course text and Moodle notes on the Normal Distribution Review this article on the Normal Distribution applied to business salary problems https://www.wallstreetmojo.com/normal-

Posted at 15:15h in Mathematics / Numerical analysis by

Review course text and Moodle notes on the Normal Distribution

Review this article on the Normal Distribution applied to business salary problems https://www.wallstreetmojo.com/normal-distribution/

1) Select one continuous variable from the Student Generated Class Database. and name the variable, 

StudentClassID:34

DegreeProgram:MBA

NumberOfDegrees:1

StatisticsPreception:Difficult

Sex:Female

NumberOfSiblings:4

CityPopulation:14493

NumberPriorStatCourses1

RateStatExperienceNovice

Do you have Children?No

Rank your comfort with using JASPDifficult 

Rank of comfort with using ExcelVery Difficult

Are your left or right handed?Right

Rate your Math ComfortabilityProficient

Tags:

2) generate ONE piece of evidence (numerical summaries, tables, or charts) that supports or refutes that the variable you selected may potentially be normally distributed.  3) attach your generated evidence (numerical summaries, tables, and/or charts) to your post,  and 4) discuss how you are justifying your claim of for or against normality be referencing your evidence.  APA formatting is ALWAYS expected. 

In your post, number your )responses (as above) so that it is clear what you are responding to

Continuous Distributions

Continous Probability Distributions: data values are measured and not counted
a probability DENSITY functions represented by mathematical functions
probabilities are calculated within ranges and not at specific values: P(a) is theoretically 0 but Excel does estimate the height of the probability density curve at 'a'
Shape Range Other
Normal Bell Shaped negative infinity to infinity mean = median
Uniform Rectangular & symmetric a to b mean = median
Exponential Skewed right 0 to infinity mean>median
Normal Distribution Benefits
Many variables in business can be represented using a normal distribution
Used to approximate discrete probability distributions
can be completely defined (with it's mathematical function) with the mean and standard deviation
N(mean, standard deviation)

normal

Calculating Normal Distribution Probabilities with Excel
Excel transforms Xi data values to Z scores before calculating probabilties
the standard normal distribution is used to determine the probablities
Use NORMDIST in Excel
Example
You need
Mean= 10
Standard Deviation = 2
STANDARDIZE NORMDIST 1-NORMDIST
Xi Z-score P(X<Xi) P(X>Xi) To find probability of ranges
7 -1.5 0.0668072013 0.9331927987 P(Xa<X<Xb)=ABS(P(X<Xb)-P(X<Xa))
5 -2.5 0.0062096653 0.9937903347
9 -0.5 0.3085375387 0.6914624613 Probability of age between 8 and 12 ?
0.6826894921

=NORMDIST(Xi, mean, s, False)

=STANDARDIZE(Xi, mean, s)

problem samples

Calculating data values of a normal distribution when the corresponding Z score or probabilities are given
WHat is the X value associated with Z-Score = 1.5?
You Need 73.75
Mean= 70
STandard Deviation = 2.5
What is the X value for the distribution where p = .35 for values less than X?
69.036698834
What is the Z-score value for the distribution where p = .35 for values less than Z?
-0.3853204664

=NORMINV(p, mean, s)

=NORMSINV(p)

=mean + Z(s)

normality

Is the Data distribution approximately normal?
check the histogram
examine the descriptive statistics
use a normality plot
Plot A Plot B
Mean and median should be near equal bell-shaped histogram
Dots are close to line
Suggests the distribution is approximately normal in shape

Empirical Rule

Need a bell-shaped distribution to use the Empirical Rule
Age
80 Age Desciptive Statistics Approximately:
91 68% of data values are within 1 standard deviation of the mean
77 Mean 79
85 Standard Deviation 9.5694384163 95% of data values are within 2 standard deviation of the mean
71
89 99.7% of data values are within 3 standard deviations of the mean
82
79
74
68 Question1: Approximately what percent of the age data is within 1 standard deviation unit of the mean?
103 According to the Empirical Rule, approximately 68% of the age
92 data is within 1 standard deviation above and below the mean
85
81 Question2: Within what interval are approximately 68% of the age data values? (Hint: need standard deviation of the distirbution)
82 According to the Empirical Rule
64 lower bound 69.5352344046
81 upper bound 88.6741112372
84
100
86
83
67
84
78
63
70
85
99
93
79
88
69
86
103
85
73
61
71
89
98
71
81
83
81
69
65
77
82
80
78
60
71
71
73
86
84
79
77
85
72
83
89
85
91
73
76
87
73
86
85
78
94
79
76
79
76
64
78
65
71
72
68
81
84
77
68
70
82
66
81
82
79
55
99
68
74
80
76
89
69
79

Generating data

Generate Normal distribution of data in Excel
Mean 10
Standard deviation 2
11.5819814265 Use Copy …Paste … Paste Special … Values
8.3738684914 To keep data from continuing to update due to the RAND() feature
9.0864744902
9.2572957454
9.3909571118
13.7527527534
10.8007385469
4.0893192297
8.9700785395
9.2928090436
8.8604097223
6.4852175137

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Chapter 5 and 6 notes Discrete and Continuous Probability Distributions

Discrete Probability Distributions