Scores on the Wechsler Adult intelligence Scale (a standard ID test) for certain age group are normally distributed with mean μ = 100 and standard deviation σ = 15. (Find the Z score/s for each question first, and then use Table A-2 at the back of your book to find the following probabilities). Show your work. D. MENSA is an elite organization that admits as members' people who score in the top 2% on IQ tests. What score on the Wchsler Adult Intelligence Scale would an individual have to earn to qualify for MENSA membership? E. Find the first quartile (Q1)? Hint: (Q1 separates the bottom 25%) ## Negative z Scores### TABLE A-2: Standard Normal (z) Distribution: Cumulative Area from the LEFTThis table provides the cumulative area from the left under the standard normal curve for negative z-scores. The table is structured as follows:- **z-Score Values:** The first column represents negative z-scores ranging from -3.4 to 0.0 in increments of 0.1.- **Columns (from .00 to .09):** These columns represent further decimal points of the z-score, allowing more precise calculations.For example, the cumulative area for a z-score of -1.5 and a second decimal of .03 is 0.0630.#### Graph Description:The graph above the table illustrates the standard normal distribution curve. The curve is symmetrical about the mean (z = 0) and highlights the area to the left of a negative z-score.### Additional Notes:- **Values Below -3.49:** For z-scores less than -3.49, use 0.0001 for the area.- **Common Interpolated Values:** - z Score: -1.645, Area: 0.0500 - z Score: -2.575, Area: 0.0050These interpolations are used when exact values are between those displayed in the table.

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Description: Scores on the Wechsler Adult intelligence Scale (a standard ID test) for certain age group are normally distributed with mean μ = 100 and standard deviation σ = 15. (Find the Z score/s for each question first, and then use Table A-2 at the back of y

Solution: It is given that the scores on the Wechsler Adult intelligence Scale (a standard ID test)…

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Scores on the Wechsler Adult intelligence Scale (a standard ID test) for certain age group are normally distributed with mean μ = 100 and standard deviation σ = 15. (Find the Z score/s for each question first, and then use Table A-2 at the back of your book to find the following probabilities). Show your work.

D. MENSA is an elite organization that admits as members' people who score in the top 2% on IQ tests. What score on the Wchsler Adult Intelligence Scale would an individual have to earn to qualify for MENSA membership?

E. Find the first quartile (Q1)? Hint: (Q1 separates the bottom 25%)

## Negative z Scores

### TABLE A-2: Standard Normal (z) Distribution: Cumulative Area from the LEFT

This table provides the cumulative area from the left under the standard normal curve for negative z-scores. The table is structured as follows:

- **z-Score Values:** The first column represents negative z-scores ranging from -3.4 to 0.0 in increments of 0.1.
- **Columns (from .00 to .09):** These columns represent further decimal points of the z-score, allowing more precise calculations.

For example, the cumulative area for a z-score of -1.5 and a second decimal of .03 is 0.0630.

#### Graph Description:
The graph above the table illustrates the standard normal distribution curve. The curve is symmetrical about the mean (z = 0) and highlights the area to the left of a negative z-score.

### Additional Notes:

- **Values Below -3.49:** For z-scores less than -3.49, use 0.0001 for the area.
- **Common Interpolated Values:**
- z Score: -1.645, Area: 0.0500
- z Score: -2.575, Area: 0.0050

These interpolations are used when exact values are between those displayed in the table.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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