# Z-score

1. What is the normal distribution/curve? What are the important properties of the standard normal curve? Why is the standard normal curve important to predicting values?

2. Define a z-score. What two pieces of information does this give you about the raw score?

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3. A sample of university students has an average GPA of 2.78 with a standard deviation of 0.45. If GPA is normally distributed, what percentage of the students has GPAs

 Z score Area a. less than 2.30 b. less than 2.00 c. more than 2.00 d. more than 3.00 e. between 2.50 and 3.50 f. between 2.00 and 2.50

4. For the distribution of GPAs described in Question 3, what is the probability that a randomly selected student will have a GPA

 Z score Probability a. less than 3.40 b. less than 3.78 c. more than 3.50 d. more than 2.50 e. between 2.00 and 3.00 f. between 3.00 and 3.50

5. A researcher wanted to learn something about the religious affiliation of the students at the local college (e.g., what percent were Catholic, Jewish, etc.). This information was not available from the Registrar and the researcher was working with a very limited budget. Therefore, she used the principle of EPSEM to select a group of 200 students, called each of them at home, and conducted a brief interview. She was able to develop many conclusions based on this information. For example, she found that 50 of the 200 respondents were Catholic and concluded that about 25% of students at the college would claim the same religious affiliation.

Identify each of the following elements in this research scenario and explain their importance:

a. Population b. Sample c. Parameter d. Statistic e. EPSEM f. Representative

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