## Normal curve and z scores (70 pts possible)

**Homework 4:**

**normal curve and z scores (70 pts possible)**

This homework requires both your text and your calculator. The objective of your fifth homework assignment involves answering questions related to the normal and standard normal curves. Excel will not be a part of the assignment this week. **Instead, you will submit this assignment as a Word document.** You will need to use the “Normal Curve Table” in Table A-1 of the Appendix of your text that is gone over in detail (with examples) in Chapter 3. First, be sure you view the PointCast presentation for this week, found in the Course Content under Module 5. This presentation provides information and goes through the steps you will need to be familiar with in order to complete this assignment. The standard normal curve is provided here to the right for your reference. **Be sure to show your work in each problem.**

1. Reading readiness of preschoolers from an impoverished neighborhood (n = 20) was measured using a standardized test. Nationally, the mean on this test for preschoolers is 30.9, with SD = 2.08.

a. Children below the 30^{th} percentile (in the bottom 30%) are in need of special assistance prior to attending school. What raw score marks the cut-off score for these children? (8 pts)

b. What percentage of children score between 25 and 28.5? (8 pts)

c. *How many* children would we expect to find with scores between 28 and 31.5?

(8 pts)

d. Children in the top 25% are considered accelerated readers and qualify for different placement in school. What raw score would mark the cutoff for such placement? (11 pts)

- Age at onset of dementia was determined for a sample of adults between the ages of 60 and 75. For 15 subjects, the results were ΣX = 1008, and Σ(X-M)
^{2}= 140.4. Use this information to answer the following:

a. What is the mean and SD for this data? (8 pts)

b. Based on the data you have and the Normal Curve Tables, what percentage of people might start to show signs of dementia at or before age 62? (8 pts)

c. If we consider the normal range of onset in this population to be +/-1 z-score from the mean, what two ages correspond to this? (8 pts)

d. A neuropsychologist is interested only in studying the most deviant portion of this population, that is, those individuals who fall within the top 10% and the bottom 10% of the distribution. She must determine the ages that mark these boundaries. What are these ages? (11 pts)