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). A. What percent of IQ scores are less than 122?B. What is the probability that a randomly selected adult in this age group has an IQ score higher than 147? Is this a significant/unusual event? Explain.C. What percent of adults in this age group have IQs between 85 and 100? Is this significant/unusual event? Explain. # Negative z Scores## TABLE A-2 Standard Normal (z) Distribution: Cumulative Area from the LEFTThis table provides the cumulative area from the left for negative z scores in a standard normal distribution. This is useful for statistical analysis and probability calculations that involve normal distributions.### Table Structure- **z Score**: The leftmost column lists z scores ranging from -3.5 and lower up to -0.0. These are negative values representing standard deviations below the mean in a standard normal distribution.- **Columns .00 to .09**: These columns provide the cumulative area from the far left of the standard normal distribution to the specified z score, broken down to two decimal places.### DiagramA bell curve diagram is displayed above the table, illustrating the normal distribution. The yellow shaded area represents the cumulative probability to the left of a z score, denoting the area of interest when using this table.### Table Data Example- For a **z score of -1.5**: - At .00, the area is **0.0668** - At .01, the area is **0.0665** - At .02, the area is **0.0643**, and so on.### Special Notes- Values for **z** below -3.49 should use 0.0001 for the area.- Commonly interpolated values are highlighted: - **z Score: -1.645, Area: 0.0500** - **z Score: -2.575, Area: 0.0050**This table continues beyond the section shown, indicating more comprehensive coverage of z scores for broader statistical evaluations.

Given, Mean μ=100 Standard deviation σ=15a)P(x<122)=Px-μσ<122-μσ =Pz<122-10015…

Answered: What percent of IQ scores are less than…

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ISBN:9781119256830

Author:Amos Gilat

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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).

A. What percent of IQ scores are less than 122?

B. What is the probability that a randomly selected adult in this age group has an IQ score higher than 147? Is this a significant/unusual event? Explain.

C. What percent of adults in this age group have IQs between 85 and 100? Is this significant/unusual event? Explain.

# Negative z Scores

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

This table provides the cumulative area from the left for negative z scores in a standard normal distribution. This is useful for statistical analysis and probability calculations that involve normal distributions.

### Table Structure

- **z Score**: The leftmost column lists z scores ranging from -3.5 and lower up to -0.0. These are negative values representing standard deviations below the mean in a standard normal distribution.
- **Columns .00 to .09**: These columns provide the cumulative area from the far left of the standard normal distribution to the specified z score, broken down to two decimal places.

### Diagram

A bell curve diagram is displayed above the table, illustrating the normal distribution. The yellow shaded area represents the cumulative probability to the left of a z score, denoting the area of interest when using this table.

### Table Data Example

- For a **z score of -1.5**:
- At .00, the area is **0.0668**
- At .01, the area is **0.0665**
- At .02, the area is **0.0643**, and so on.

### Special Notes

- Values for **z** below -3.49 should use 0.0001 for the area.
- Commonly interpolated values are highlighted:
- **z Score: -1.645, Area: 0.0500**
- **z Score: -2.575, Area: 0.0050**

This table continues beyond the section shown, indicating more comprehensive coverage of z scores for broader statistical evaluations.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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