PS296 Lecture Notes - Lecture 6: Mode 7, Formula 4, Percentile Rank
Steps Involved in Answering a Z Score Question:
1) record all values that are given in the question
2) draw a picture and shade in the area you are interested in looking up, helps when it comes time to
look up the probability in the chart given the z score
3) write down the appropriate formula
4) sub the known values into the formula
5) solve the formula
6) look up appropriate value in table E.10
7) write a concluding statement that answers the question
Example:
Steve's score: 6
Jane: 9
Chris: 7
Ellen: 8
Jacob: 7
Mean = 7.4
Median = 7
Mode = 7
Std dev = 1.140
Variance = 1.3
Range = 3
x = 8 (ellen's score)
µ = 7.4
σ = 1.140
-interested in Ellen's score or higher, thus looking at the smaller portion (to the right side of mean)
z = 8 – 7.4 / 1.14 = .526
Table E.10: z value of .53, probability of smaller portion is .2981
The probability of obtaining the same score as Ellen or higher is .30.
What is the probability of obtaining a score between Chris and Jane?
Z = 7 – 7.4 / 1.140 = -0.351
Z = 9 – 7.4 / 1.140 = 1.404
-the z score represents x to the MEAN, they overlap with the mean,
The probability of the larger portion of z = .35 is .6368 and the probability of the smaller portion of z =
1.40 is .0808. The difference between these scores is .6368 - .0808 = .556
The probability of obtaining a score between Chris and Jane is .56.
Document Summary
Range = 3 x = 8 (ellen"s score) Interested in ellen"s score or higher, thus looking at the smaller portion (to the right side of mean) z = 8 7. 4 / 1. 14 = . 526. Table e. 10: z value of . 53, probability of smaller portion is . 2981. The probability of obtaining the same score as ellen or higher is . 30. Z = 7 7. 4 / 1. 140 = -0. 351. Z = 9 7. 4 / 1. 140 = 1. 404. The z score represents x to the mean, they overlap with the mean, The probability of the larger portion of z = . 35 is . 6368 and the probability of the smaller portion of z = The difference between these scores is . 6368 - . 0808 = . 556. The probability of obtaining a score between chris and jane is . 56. Stefanie is thinking about attending graduate school, and therefore signed up to write her graduate. She scored 160 on the quantitative section of the test.
