z-scores Worksheet

1) Beneath the graph, label SD and z-scores.

SD

z-score

2) Beneath the graph, label SD and z-scores.

SD

z-score

3) If you have an IQ score of 120, what proportion of the population has a higher IQ than you do?

Note: IQ tests are usually standardized so they have a mean of 100 and standard deviation of 15.

Show all your work, including a clearly labeled graph.

What proportion of the area under the curve is located between

B and C? C and D? A and C? A and B? D and E? A and D?

What proportion of the area under the curve is located between

C and D? B and C? B and D? A and D? A and B? A and E? A and F? C and F?

4) Using the information below, what is the value of zobt?

X = 45 μ = 48 σ = 2

What proportion of scores is below 45? Draw a picture.

6) Your friend tells you she scored 92 on her last exam. You were pretty impressed until you learned that the mean score in the entire class was 95, with a standard deviation of 1.

What is the z-score that corresponds with your friend’s

raw score?

What percentile does your friend’s performance put her

in on this exam?

5) The average person in the U.S.A. spends = 300 minutes watching television each day. Assume that the distribution of television watching is normal with a standard deviation of = 120 minutes.

What proportion of viewers spends fewer than 60 minutes a day watching television?

What percentile is someone in who watches 60 minutes a day?