Please help with abc :) **Title: Understanding the Distribution of Walking Ages in Children****Introduction:**Consider the age at which children typically learn to walk. This age is normally distributed with a mean of 11 months and a standard deviation of 1.2 months. A study involving 13 randomly selected individuals records the age at which they learned to walk. The following questions explore the statistical properties of this distribution.**a. Distribution of Individual Walking Ages (X):**We start by exploring the distribution of individual ages (X) when children learn to walk:- Distribution: $ X \sim N(\mu, \sigma^2) $- Values: Mean ($\mu$) = 11, Standard Deviation ($\sigma$) = 1.2**b. Distribution of Sample Mean (x̄):**Next, we examine the distribution of the average walking age for a sample of 13 individuals (x̄):- Distribution: $ \bar{x} \sim N\left(\mu, \frac{\sigma}{\sqrt{n}}\right) $- Values: Mean ($\mu$) = 11, Standard Deviation = $\frac{1.2}{\sqrt{13}}$**c. Probability for an Individual Age:**Compute the probability that a randomly selected individual learned to walk between 9.5 and 12 months:- Probability: [Calculated value]**d. Probability for Sample Mean:**For 13 individuals, calculate the probability that their average walking age lies between 9.5 and 12 months:- Probability: [Calculated value]**e. Requirement for Normal Distribution:**Assess the necessity of assuming a normal distribution in part d:- Necessary: Yes/No**f. Interquartile Range (IQR) for Sample Mean:**Lastly, find the Interquartile Range (IQR) for the sample mean walking age for groups of 13 people:- Q1: [Value] months- Q3: [Value] months- IQR: [Value] months**Conclusion:**This analysis uses statistical methods to understand typical walking ages in children and demonstrates the application of normal distribution in real-world scenarios.

Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case you required unanswered sub parts also, kindly re-post those parts separately.a. Let X be the age that children learn to walk. From the given information, X follows normal distribution with mean µ=11 months and a standard deviation σ=1.2 month. Then, the distribution of X is normal.b. If X follows normal distribution with mean µ and a standard deviation σ, then x-bar follows normal distribution with mean µ and a standard deviation σ/(square root of n). From the given information, n=13. Then, the distribution of x-bar is normal. Thus,c. The probability that the one randomly selected person learned to walk when the person was between 9.5 and 12 months old is Thus, the probability that the one randomly selected person learned to walk when the person was between 9.5 and 12 months old is 0.6910.

Math

Statistics

Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 1.2 month. 13 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( b. What is the distribution of ? - N( c. What is the probability that one randomly selected person learned to walk when the person was between 9.5 and 12 months old? d. For the 13 people, find the probability that the average age that they learned to walk is between 9.5 and 12 months old. e. For part d), is the assumption that the distribution is normal necessary? O YesO No f. Find the IQR for the average first time walking age for groups of 13 people. Q1 = months Q3 = months IQR: months

Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 1.2 month. 13 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( b. What is the distribution of ? - N( c. What is the probability that one randomly selected person learned to walk when the person was between 9.5 and 12 months old? d. For the 13 people, find the probability that the average age that they learned to walk is between 9.5 and 12 months old. e. For part d), is the assumption that the distribution is normal necessary? O YesO No f. Find the IQR for the average first time walking age for groups of 13 people. Q1 = months Q3 = months IQR: months

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

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Please help with abc :)

**Title: Understanding the Distribution of Walking Ages in Children**

**Introduction:**

Consider the age at which children typically learn to walk. This age is normally distributed with a mean of 11 months and a standard deviation of 1.2 months. A study involving 13 randomly selected individuals records the age at which they learned to walk. The following questions explore the statistical properties of this distribution.

**a. Distribution of Individual Walking Ages (X):**

We start by exploring the distribution of individual ages (X) when children learn to walk:

- Distribution: $ X \sim N(\mu, \sigma^2) $
- Values: Mean ($\mu$) = 11, Standard Deviation ($\sigma$) = 1.2

**b. Distribution of Sample Mean (x̄):**

Next, we examine the distribution of the average walking age for a sample of 13 individuals (x̄):

- Distribution: $ \bar{x} \sim N\left(\mu, \frac{\sigma}{\sqrt{n}}\right) $
- Values: Mean ($\mu$) = 11, Standard Deviation = $\frac{1.2}{\sqrt{13}}$

**c. Probability for an Individual Age:**

Compute the probability that a randomly selected individual learned to walk between 9.5 and 12 months:

- Probability: [Calculated value]

**d. Probability for Sample Mean:**

For 13 individuals, calculate the probability that their average walking age lies between 9.5 and 12 months:

- Probability: [Calculated value]

**e. Requirement for Normal Distribution:**

Assess the necessity of assuming a normal distribution in part d:

- Necessary: Yes/No

**f. Interquartile Range (IQR) for Sample Mean:**

Lastly, find the Interquartile Range (IQR) for the sample mean walking age for groups of 13 people:

- Q1: [Value] months
- Q3: [Value] months
- IQR: [Value] months

**Conclusion:**

This analysis uses statistical methods to understand typical walking ages in children and demonstrates the application of normal distribution in real-world scenarios.

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