# Standardized Scores

1. Given a mean of 60, with a standard deviation of 12, and with a raw score of 75, find:

(a) the z-score

(b) percentile rank

(c) t-score

(d) SAT score

(e) stanine score

2. Sammy Slicko bets that he can flip a coin and come up heads every time. At what point in the coin toss (5 in a row, 6 in a row, or 7 in a row), can we present a case that the coin is rigged?

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#### Solution Preview

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Use has been made of information at http://edtech.kennesaw.edu/dataanalysis/explaintestscores.htm for answering the questions

1. Given a mean of 60, with a standard deviation of 12, and with a raw score of 75, find:

(a) the z-score

Raw score=x= 75

Mean=M= 60

Standard deviation =s= 12

z=(x-M)/s= 1.25 =(75-60) / 12

Answer: 1.25

(b) percentile rank

"A percentile score indicates the percentage of people an individual did better than in a reference group. Example: A person scoring at the 84th percentile did better than 84% of those in the norming or reference group.

"

z= 1.25

Probability value corresponding to Z = 1.25 = 0.8944 0r 89.44%

Percentile ...

#### Solution Summary

Standardized Scores (z-score, percentile rank, t-score, SAT score, stanine score) are calculated, given mean, standard deviation and raw score.