Loading presentation...

Present Remotely

Send the link below via email or IM

Copy

Present to your audience

Start remote presentation

  • Invited audience members will follow you as you navigate and present
  • People invited to a presentation do not need a Prezi account
  • This link expires 10 minutes after you close the presentation
  • A maximum of 30 users can follow your presentation
  • Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

DeleteCancel

Z Score Workshop

No description
by

Taylor Landrie

on 22 July 2016

Comments (0)

Please log in to add your comment.

Report abuse

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
For more information, contact Germanna Tutoring Services:
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