# – Please follow the instructions and make sure you have answered all questions 1

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– Please follow the instructions and make sure you have answered all questions

1. Use the random decimal fraction generator at Random.org to generate a list of three fractions with four decimal places. Assume those decimal fractions represent probability values associated with z-scores. Then use the standard normal table (z-table) to look up the z-score that is closest to matching with that probability and list them below. (Here is the link for the random number generator link. https://www.random.org/integers/)

a probability value (generated fraction) =

associated z-score =

a probability value (generated fraction) =

associated z-score =

a probability value (generated fraction) =

associated z-score =

2. Why do researchers convert distributions of data to standard scores? How is this useful to researchers?

3. Give an example of a continuous probability distribution and explain why it is considered continuous.

4. Assume a data set has µ = 475 and σ = 40. If you were to take repeated random samples of n = 25 from that data set, what would be the expected value of the mean of the sampling distribution of the sample means? Explain how you determined that, i.e., how do you know this?

5. Mary took a physics test and scored a 61. The class average was 52 and the standard deviation was 6. Sheila took a chemistry test and scored a 74. The class average was 64 and the standard deviation was 8. Who performed better? What is the rationale for your answer, i.e., how do you know this?

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