Note: Question A to C was answered alreadyNeed assistance answering qestion E to G IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X= IQ of an individual.(a) Find the z-score for an IQ of 118, rounded to three decimal places. (b) Find the probability that the person has an IQ greater than 118. (c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (a), rounded to one decimal place).Shade:. Click and drag the arrows to adjust the values. 1.2 ### (g) Sketch the Graph and Write the Probability StatementIn this exercise, you are required to sketch a graph and compose a probability statement based on the given mathematical or statistical problem. Below is the empty editor workspace where you will create your graph and input the associated probability statement.#### Editor Instructions:- Utilize the toolbar options for drawing and formatting the content.- **Text Formatting:** Bold (`B`), Italic (`I`), Underline (`U`).- **Scripts and Equations:** Subscript (`_`), Superscript (`x^2`), and special characters (`Ω` symbol).- **Insertion Tools:** Link (` ### IQ Distribution and Mensa Membership Qualification#### MENSA Membership Criteria(d) **MENSA** is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization. \[ \text{Minimum IQ:} \space \underline{\hspace{2cm}} \]#### Probability and IQ Distribution Graph(e) **Sketch the graph, and write the probability statement.**Below, you should provide a graph that illustrates the normal distribution of IQ scores, with the top 2% highlighted to represent the MENSA qualification threshold.Additionally, include the appropriate probability statement indicating the IQ value $ X $ that corresponds to this threshold.#### Middle 50% IQ Range(f) **The middle 50% of IQs fall between what two values?**\[ \underline{\hspace{4cm}} \space - \space \underline{\hspace{4cm}} \] In this section, determine the IQ range that contains the middle 50% of the population, which corresponds to the interquartile range (IQR).**Note:** Please note that specific calculations and detailed illustrations are necessary to complete sections (d) and (f), which typically involve the use of statistical tools and knowledge of normal distribution properties.

Individuals with top 2% IQ has an IQ of more than 130.80.

Answered: (d) MENSA is an organization whose…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Note: Question A to C was answered already

Need assistance answering qestion E to G

IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X= IQ of an individual.

(a) Find the z-score for an IQ of 118, rounded to three decimal places.

(b) Find the probability that the person has an IQ greater than 118.

(c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (a), rounded to one decimal place).
Shade:

. Click and drag the arrows to adjust the values.

1.2

### (g) Sketch the Graph and Write the Probability Statement

In this exercise, you are required to sketch a graph and compose a probability statement based on the given mathematical or statistical problem. Below is the empty editor workspace where you will create your graph and input the associated probability statement.

#### Editor Instructions:
- Utilize the toolbar options for drawing and formatting the content.
- **Text Formatting:** Bold (`B`), Italic (`I`), Underline (`U`).
- **Scripts and Equations:** Subscript (`_`), Superscript (`x^2`), and special characters (`Ω` symbol).
- **Insertion Tools:** Link (`

### IQ Distribution and Mensa Membership Qualification

#### MENSA Membership Criteria
(d) **MENSA** is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization.

\[ \text{Minimum IQ:} \space \underline{\hspace{2cm}} \]

#### Probability and IQ Distribution Graph
(e) **Sketch the graph, and write the probability statement.**

Below, you should provide a graph that illustrates the normal distribution of IQ scores, with the top 2% highlighted to represent the MENSA qualification threshold.

Additionally, include the appropriate probability statement indicating the IQ value $ X $ that corresponds to this threshold.

#### Middle 50% IQ Range
(f) **The middle 50% of IQs fall between what two values?**

\[ \underline{\hspace{4cm}} \space - \space \underline{\hspace{4cm}} \]

In this section, determine the IQ range that contains the middle 50% of the population, which corresponds to the interquartile range (IQR).

**Note:** Please note that specific calculations and detailed illustrations are necessary to complete sections (d) and (f), which typically involve the use of statistical tools and knowledge of normal distribution properties.

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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