# Z Score Practice

**Topics:**Normal distribution, Standard deviation, Standard score

**Pages:**2 (308 words)

**Published:**April 2, 2013

Z-Score Practice

1. When raw scores from normal distribution are converted to standard scores, the resulting distribution has a mean equal to ________ and SD equal to _________.

2. Scores on a particular test are normally distributed with a mean of 70 and an SD of 15. Between what two scores would you expect?

a. 68% of the scores to fall between ____________ and _____________? b. 95% of the scores to fall between ____________ and _____________?

3. A distribution of scores has a mean of 70 and an SD of 5. The following four scores were drawn from that distribution: 58, 65, 73 and 82.

a. Transform the raw scores to standard scores.

b. Calculate the percentile for each score (percentage below the score).

4. According to documented norms, the distribution of gestation time is approximately normal with mean 266 days and SD 16 days.

a. What is the probability (percentage) that a baby has a gestation time greater than 280 days?

b. What is the probability (percentage) that a baby has a gestation time less than 250 days?

c. What is the probability (percentage) that a baby has a gestation time between 242 and 270 days?

5. The average time between infection with the AIDS virus and developing AIDS has been estimated to be 8 years with a standard deviation of about 2 years. Approximately what fraction of people develop AIDS within 4 years of infection? a. 5%

b. 2.5%

c. 32%

d. 16%

e. 1%

6. The distribution of the heights of students in a large class is roughly bell-shaped. Moreover, the average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches. Thus, the standard deviation of the height distribution is approximately equal to:

a. 2

b. 3

c. 6

d. 9

e. 12

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