**Understanding Quartiles in a Normal Distribution**Assume that adults have IQ scores that are normally distributed with a mean of 101.5 and a standard deviation of 24.3. We want to find the first quartile \( Q_1 \), which is the IQ score separating the bottom 25% from the top 75%.The first quartile is represented by a specific value on the IQ scale. In a normal distribution, this can be found using statistical methods or software that handles standard normal distribution calculations.**Steps to Find the First Quartile:**1. **Draw a Normal Distribution Graph**: Visualize or draw a bell curve depicting the normal distribution with mean 101.5. The x-axis represents IQ scores.2. **Locate \( Q_1 \)**: The first quartile is the point on the x-axis where 25% of the data lies to the left. Graphing this can help illustrate how data is distributed.3. **Calculate \( Q_1 \)** using the formula for the z-score: \[ Q_1 = \mu + z \times \sigma \] where \( \mu = 101.5 \) (the mean), \( \sigma = 24.3 \) (the standard deviation), and \( z \) is the z-score associated with the first quartile in a standard normal distribution (approximately -0.674).4. **Result Interpretation**: Once calculated, \( Q_1 \) will give the IQ score below which 25% of adult IQ scores may be expected to fall.**The first quartile is:** \(\_\_\_\) (Type an integer or decimal rounded to one decimal place as needed.)This exercise illustrates how quartiles are used to interpret data distribution, particularly in understanding how scores compare within a population.

Find z-value: Use excel formula "=NORM.S.INV(0.25)" to find the z-score.

Assume that adults have IQ scores that are normally distributed with a mean of 101.5 and a standard deviation 24.3. Find the first quartile Q,, which is the IQ score separating the bottom 25% from the top 75%. (Hint: Draw a graph.) The first quartile is (Type an integer or decimal rounded to one decimal place as needed.)

Assume that adults have IQ scores that are normally distributed with a mean of 101.5 and a standard deviation 24.3. Find the first quartile Q,, which is the IQ score separating the bottom 25% from the top 75%. (Hint: Draw a graph.) The first quartile is (Type an integer or decimal rounded to one decimal place as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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