Assume that adults have IQ score that are normally distributed with a mean of 100.4 and a standard deviation of 19.1. Find the probability that a randomly selected adult has an IQ greater than 130.7 (hint draw a graph.) the probability that a randomly selected adult from this group has an IQ greater than 130.7 **Question:**Assume that adults have IQ scores that are normally distributed with a mean of 100.4 and a standard deviation of 19.1. Find the probability that a randomly selected adult has an IQ greater than 130.7. (Hint: Draw a graph.)**Solution:**To find the probability that a randomly selected adult from this group has an IQ greater than 130.7:1. **Calculate the Z-score:** \[ Z = \frac{X - \mu}{\sigma} = \frac{130.7 - 100.4}{19.1} \] where $ X $ is the IQ score of interest, $ \mu $ is the mean IQ score, and $ \sigma $ is the standard deviation.2. **Use Z-table or calculator:** Once the Z-score is calculated, use a standard normal distribution table (Z-table) or a calculator to find the probability associated with that Z-score. This probability represents the percentage of the population with IQ scores less than 130.7. Subtract this probability from 1 to find the probability of having an IQ greater than 130.7.3. **Round the result:** Round the final probability to four decimal places as needed.**Graph Explanation:**You can illustrate this problem with a normal distribution curve:- **Mean (100.4):** Mark the center of the curve.- **Standard Deviation (19.1):** Define the width of the curve.- **Area of Interest (IQ > 130.7):** Shade the area to the right of 130.7 to depict the probability you're trying to find.**Answer Entry:**- Once calculated, enter your answer in the answer box and click "Check Answer."This process will guide users through solving similar statistical problems involving normal distributions.

According to the scenario, it is assumed that adults have IQ scores that are normally distributed…

Answered: decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Assume that adults have IQ score that are normally distributed with a mean of 100.4 and a standard deviation of 19.1. Find the probability that a randomly selected adult has an IQ greater than 130.7 (hint draw a graph.)

the probability that a randomly selected adult from this group has an IQ greater than 130.7

**Question:**

Assume that adults have IQ scores that are normally distributed with a mean of 100.4 and a standard deviation of 19.1. Find the probability that a randomly selected adult has an IQ greater than 130.7. (Hint: Draw a graph.)

**Solution:**

To find the probability that a randomly selected adult from this group has an IQ greater than 130.7:

1. **Calculate the Z-score:**

\[
Z = \frac{X - \mu}{\sigma} = \frac{130.7 - 100.4}{19.1}
\]

where $ X $ is the IQ score of interest, $ \mu $ is the mean IQ score, and $ \sigma $ is the standard deviation.

2. **Use Z-table or calculator:**

Once the Z-score is calculated, use a standard normal distribution table (Z-table) or a calculator to find the probability associated with that Z-score. This probability represents the percentage of the population with IQ scores less than 130.7. Subtract this probability from 1 to find the probability of having an IQ greater than 130.7.

3. **Round the result:**

Round the final probability to four decimal places as needed.

**Graph Explanation:**

You can illustrate this problem with a normal distribution curve:

- **Mean (100.4):** Mark the center of the curve.
- **Standard Deviation (19.1):** Define the width of the curve.
- **Area of Interest (IQ > 130.7):** Shade the area to the right of 130.7 to depict the probability you're trying to find.

**Answer Entry:**

- Once calculated, enter your answer in the answer box and click "Check Answer."

This process will guide users through solving similar statistical problems involving normal distributions.

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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