Probability is an important aspect of the standard normal distribution. In this video, learn to work with the standard normal's associated probabilities.
 [Instructor] Let's explore probability and the standard normal distribution. Now the standard normal distribution is the basis for many textbook problems the involve probability. The idea is to start with any normal distribution. Then convert the scores in that distribution to zscores and find the relevant probabilities using the standard normal distribution. So if you had a statistics course, you might remember the standard normal distribution and you might remember having to solve problems involving probabilities and zscores. And example is IQ scores. IQ is normally distributed. And one version of the IQ test has a mean of 100 and a standard deviation of 16. What's the probability of finding a person whose IQ is between 100 and 116? Well the zscore for 100 equals zero because 100 is the mean. And the zscore for 116 equals one because 16 is the standard deviation. So what we're asking is what is the probability that z is between zero and one? A quick look at the graph here tells you that that's .3413. So the probability of an IQ being greater than or equal to 100 or less than or equal to 116 is .3413. What about the probability of finding a person whose IQ is between 92 and 116? Well to find the zscore for 92, we subtract 100, the mean, from 92 and divide the result by the standard deviation, which is 16. The zscore is 0.5. That's half a standard deviation unit below the mean. And if we go ahead and do the same thing for 116, we'd find that the zscore is 1.0 because 116 is one standard deviation above the mean. So the proportion of area between zero and 0.5 is .1915. The proportion of area between zero and 1.00 is .3413. So the probability the z is between 0.5 and one is .1915 plus .3413, .5328. I just gave you those proportions. How do we find these proportions? The hard way is to solve a normal distribution equation. The easier way is to use a standard normal distribution table in a statistics textbook. But the much easier way is to use Excel. And I'll show you how to do that. In cells D2 and E2, I put the zscores for our example. The objective is to find the area under the standard normal distribution between those two zscores. And we use NORM.S.DIST to do this. Now, as the headings in cells F1 and G1 tell you, NORM.S.DIST can return the area under the standard normal distribution to the left of the provided zscore. We use that area to solve this problem. So click in cell F2 and type equal norm.s.dist, click cell D2 comma and now select TRUE from the popup menu, Enter and that gives us the area to the left of 0.5. Just drag that value over into cell G2. And the desired area is the difference between G2 and F2, which matches up to the value 0.5328 that I showed you earlier. A lot of other combinations of areas are possible. And here's how NORM.S.DIST found the area for us. The area to the left of one, .8413. The area to the left of 0.5, .3085. Subtract .3085 from .8413 equals the desired area .5328.
Author
Joseph SchmullerReleased
6/11/2019 Using Excel functions and graphics
 Data types and variables
 Calculating probability
 Mean, median, and mode
 Calculating variability
 Organizing and graphing distributions
 Visualizing normal distributions
 Sampling distributions
 Making estimations
 Testing hypotheses: mean, z and ttesting, and more
 Analyzing variance
 Performing repeated measure testing
 Regression testing
 Hypotheses testing with correlation
Skill Level Beginner
Duration
Views
Related Courses

Statistics Foundations: 1
with Eddie Davila2h 6m Beginner 
Statistics Foundations: 2
with Eddie Davila1h 56m Intermediate 
Statistics Foundations: 3
with Eddie Davila1h 41m Advanced 
Excel Data Analysis: Forecasting
with Wayne Winston3h 7m Intermediate

Introduction

What is data?1m 37s

The big picture2m 11s


1. Excel Statistics Fundamentals

Using Excel functions6m 12s

Working with Excel graphics4m 23s


2. Types of Data

Differentiating data types4m 20s


3. Probability

Defining probability1m 55s

Calculating probability6m 14s


4. Central Tendency

The mean and its properties2m 16s

Working with the median2m 23s

Working with the mode1m 53s


5. Variability

Understanding variance4m 30s

Zscores3m 2s


6. Distributions

Probability distributions4m 10s

7. Normal Distributions

8. Sampling Distributions

Meeting the tdistribution2m 24s

9. Estimation

Confidence in estimation4m 45s


10. Hypothesis Testing

11. Testing Hypotheses about a Mean

12. Testing Hypotheses about a Variance

The chisquared distribution3m 37s


13. Independent Samples Hypothesis Testing

14. Matched Samples Hypothesis Testing

15. Testing Hypotheses about Two Variances

16. The Analysis of Variance

Introducing ANOVA6m 22s

Applying ANOVA1m 41s

17. After the Analysis of Variance

18. Repeated Measures Analysis

What is repeated measures?5m 48s


19. Hypothesis Testing with Two Factors

Statistical interactions5m 4s

Twofactor ANOVA5m 21s


20. Regression

Multiple regression analysis3m 16s

21. Correlation

Understanding correlation2m 39s

Conclusion

Next steps1m

 Mark as unwatched
 Mark all as unwatched
Are you sure you want to mark all the videos in this course as unwatched?
This will not affect your course history, your reports, or your certificates of completion for this course.
CancelTake notes with your new membership!
Type in the entry box, then click Enter to save your note.
1:30Press on any video thumbnail to jump immediately to the timecode shown.
Notes are saved with you account but can also be exported as plain text, MS Word, PDF, Google Doc, or Evernote.
Share this video
Embed this video
Video: Standard normal distribution probability