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# Z Score Workshop

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by

## Taylor Landrie

on 26 February 2018

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#### Transcript of Z Score Workshop

A z-score is the number of standard deviations that a given value, x, is above or below the mean.
Z-Score Workshop
If an individual value, x, is less than the mean, its z-score is a negative number. If an individual value, x, is greater than the mean, its z-score is a positive number.
Germanna Tutoring Services
What is a z-score?
Three types of
z-score problems

Less than example
Greater than example
Less than example
Calculate z-score
Greater than example
Calculate z-score
Acknowledgments
Fredericksburg Campus:
(540) 891-3017 | SP1-208

Locust Grove Campus:
(540) 423-9148 | OR-208

Online: www.germanna.edu/tutoring
Data for the number of movies people watch in a month is collected from a 100 person sample group. The sample data indicates that the mean of the sample is 15 with a sample standard deviation of 3. Find the probability that a person watches
less than
22 movies per month.
Data for the number of pieces of candy people eat in a month is collected from a 120 person sample group. If the mean of the sample is 20 and the sample standard deviation is 5, what is the probability of a person eating
less than
23 pieces of candy?
Formula:

z-score for 23 pieces of candy: z = 23-20 = 0.60
5
All of the employees of a company are asked how many books they read per month. The data collected from this population indicates that the population mean is 4.25 with a population standard deviation of 2. Find the probability for a person who reads
more than
2.5 books per month.

All of the employees at a company are asked how many hours per week they watch television. The data collected from this population results in a mean of 6 with standard deviation of 2.2. Find the probability that a person watches
more than
2.5 hours of television per week.
Formula:

z-score for 2.5 hours: z = 2.5-6 = -1.59
2.2
Z-scores correspond to a specific area under the bell curve. This area can be found in a z-score table.
Between example
Data for the number of movies people watch in a month is collected from a 100 person sample group. The sample data indicates that the mean of the sample is 15 with a sample standard deviation of 6.5. Find the probability that person watches
between
6 and 22 movies per month.
Between example
All of the students at a college are asked how many electronic devices that they own. The data collected for this population indicated that the population mean is 10 with a population standard deviation of 4.5. Find the probability that a person owns
between
2 and 12 devices.
Calculate z-score

Area = 0.7257
Probability = 0.7257
Area = 0.7761
Probability = 0.7761
Area = 0.6325
Probability = 0.6325
Use z-score table
Find area/probability
Use TI-83/84 Calculator
Press 2nd and then the Vars key.
Choose option 2: normalcdf(
Type normalcdf(-99999, 2.33)
Press Enter
The probability that a person watches less than 22 movies per month is .9901.
Calculate z-score
Find area/probability
Use TI-83/84 Calculator
Press 2nd and then the Vars key.
Choose option 2: normalcdf(
Type normalcdf(-99999, 0.60)
Press Enter
Use z-score table
Use z-score table
Finding area/probability
Use TI-83/84 Calculator
Press 2nd and then the Vars key.
Choose option 2: normalcdf(
Type normalcdf(-0.88,99999)
Press Enter
The probability that a person reads more than 2.5 books a month is 0.8106.
Find area/probability
Use z-score table
Use TI-83/84 Calculator
Press 2nd and then the Vars key.
Choose option 2: normalcdf(
Type normalcdf(-1.38, 1.08)
Press Enter
The probability that someone watches between 6 and 22 movies per month is 0.7761.
Calculate z-score
Formula:

z-score for 6 movies: z = 6-15=-1.38
6.5
z-scores for 22 movies: z = 22-15 = 1.08
6.5
1-0.1894 to find the area to the right of a -0.88 z-score.
Find area/probability
Use TI-83/84 Calculator
Press 2nd and then the Vars key.
Choose option 2: normalcdf(
Type normalcdf(-1.59,99999)
Press Enter
Use z-score table
1-0.0559 to find the area to the right of a -1.59 z-score.
In order to find the area between two z-scores, take the area of the right most z-score (1.08) and subtract the area of the left most z-score (-1.38) from it. Thus we would do 0.8599-0.0838 to find the area between our two z-scores.
Formula:

z-score for 2 devices: z = 2-10 = -1.78
4.5

z-score for 12 devices: z = 12-10 = 0.44
4.5

Find area/probability
Use z-score table
In order to find the area between two z-scores, take the area of the right most z-score (0.44) and subtract the area of the left most z-score (-1.78) from it. Thus we would do 0.6700-0.0375 to find the area between our two z-scores.
Use TI-83/84 Calculator
Press 2nd and then the Vars key.
Choose option 2: normalcdf(
Type normalcdf(-1.78, 0.44)
Press Enter
Information about z-score properties and images of z-score tables obtained from:

Triola, Mario F.
Elementary Statisics, 12th
edition
. Boston, MA: Pearson Education,
Inc. E-book.
Less than
Greater than
Between
Formula:

z-score for 22 movies: z = 22-15 = 2.33
3
Z-score = 2.33
z-score=0.60
The probability that a person eats less than 23 pieces of candy is 0.7257.
z-score = -0.88
z-score = -1.59
0.9441 probability that a person watches more than 2.5 hours of television a week.
Calculate z-score
Formula:

z-score for 2.5 books: z = 2.5-4.25 = -0.88
2
The probability that a person owns between 2 and 12 devices is 0.6235
z-score = -1.38
z-score = 1.08
Z-score formula
z-score = -1.78
z-score = 0.44
z-score for population:
z-score for sample:
Full transcript