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Practice A research was interested in the relation between stress and humor. Below are data from 8 subjects who completed tests of these two traits. Are these two variables related to each other? How much stress would a person probably experience if they had no sense of humor (i.e., score = 0)? How about if they had a high level of humor (i.e., score = 15)? Stress Sense of Humor 4 2 10 8 12 11 5 3 7 8 6 7 2 3 14 13
Practice • r = .91 • Y = .77 + .98(Humor) • .77 = .77 + .98(0) • 15.47 = .77 + .98(15) • You don’t want to have a sense of humor
What is the probability of picking an ace? 4 / 52 = .077 or 7.7 chances in 100
(.077) + (.077) + (.077) + (.077) = .308 16 / 52 = .308
What is the probability of getting a 2 and then after replacing the card getting a 3 ?
What is the probability that the two cards you draw will be a black jack?
10 Card = (.077) + (.077) + (.077) + (.077) = .308 Ace after one card is removed = 4/51 = .078 (.308)*(.078) = .024
Practice • What is the probability of rolling a “1” using a six sided dice? • What is the probability of rolling either a “1” or a “2” with a six sided dice? • What is the probability of rolling two “1’s” using two six sided dice?
Practice • What is the probability of rolling a “1” using a six sided dice? 1 / 6 = .166 • What is the probability of rolling either a “1” or a “2” with a six sided dice? • What is the probability of rolling two “1’s” using two six sided dice?
Practice • What is the probability of rolling a “1” using a six sided dice? 1 / 6 = .166 • What is the probability of rolling either a “1” or a “2” with a six sided dice? (.166) + (.166) = .332 • What is the probability of rolling two “1’s” using two six sided dice?
Practice • What is the probability of rolling a “1” using a six sided dice? 1 / 6 = .166 • What is the probability of rolling either a “1” or a “2” with a six sided dice? (.166) + (.166) = .332 • What is the probability of rolling two “1’s” using two six sided dice? (.166)(.166) = .028
Next step • Is it possible to apply probabilities to a normal distribution?
Theoretical Normal Curve -3 -2 -1 1 2 3
Theoretical Normal Curve -3 -2 -1 1 2 3 Z-scores -3 -2 -1 0 1 2 3
We can use the theoretical normal distribution to determine the probability of an event. For example, do you know the probability of getting a Z score of 0 or less? .50 -3 -2 -1 1 2 3 Z-scores -3 -2 -1 0 1 2 3
We can use the theoretical normal distribution to determine the probability of an event. For example, you know the probability of getting a Z score of 0 or less. .50 -3 -2 -1 1 2 3 Z-scores -3 -2 -1 0 1 2 3
With the theoretical normal distribution we know the probabilities associated with every z score! The probability of getting a score between a 0 and a 1 is .3413 .3413 .1587 .1587 -3 -2 -1 1 2 3 Z-scores -3 -2 -1 0 1 2 3
What is the probability of getting a score of 1 or higher? .3413 .3413 .1587 .1587 -3 -2 -1 1 2 3 Z-scores -3 -2 -1 0 1 2 3
These values are given in Table C on page 390 .3413 .3413 .1587 .1587 -3 -2 -1 1 2 3 Z-scores -3 -2 -1 0 1 2 3
To use this table look for the Z score in column AColumn B is the area between that score and the mean Column B .3413 .3413 .1587 .1587 -3 -2 -1 1 2 3 Z-scores -3 -2 -1 0 1 2 3
To use this table look for the Z score in column AColumn C is the area beyond the Z score Column C .3413 .3413 .1587 .1587 -3 -2 -1 1 2 3 Z-scores -3 -2 -1 0 1 2 3
The curve is symmetrical -- so the answer for a positive Z score is the same for a negative Z score Column B Column C .3413 .3413 .1587 .1587 -3 -2 -1 1 2 3 Z-scores -3 -2 -1 0 1 2 3
Practice • What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? • Between mean and z = .56? • Beyond z = 2.25? • Between the mean and z = -1.45
Practice • What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? • Between mean and z = .56? .2123 • Beyond z = 2.25? • Between the mean and z = -1.45
Practice • What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? • Between mean and z = .56? .2123 • Beyond z = 2.25? .0122 • Between the mean and z = -1.45
Practice • What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? • Between mean and z = .56? .2123 • Beyond z = 2.25? .0122 • Between the mean and z = -1.45 .4265
Practice • What proportion of this class would have received an A on the last test if I gave A’s to anyone with a z score of 1.25 or higher? • .1056
Note • This is using a hypothetical distribution • Due to chance, empirical distributions are not always identical to theoretical distributions • If you sampled an infinite number of times they would be equal! • The theoretical curve represents the “best estimate” of how the events would actually occur
PROGRAM http://www.jcu.edu/math/isep/Quincunx/Quincunx.html
Theoretical Normal Curve Normality frequently occurs in many situations of psychology, and other sciences
Practice • #7.7 • #7.8
