Can you please answer this question and all of the sub problems and show all of the steps to the solution ### Statistical Analysis of Ages of Multiple-Birth MothersConsider the scenario where the ages of mothers giving birth to multiple babies (three or more) are normally distributed. According to the given data:- **Mean Age**: 31.7 years- **Standard Deviation**: 5.2 yearsBased on this distribution, we can answer the following questions:#### a. Percentage of Mothers Between Ages 30 to 35To find out what percent of these mothers are between the ages of 30 and 35:\[ P(30 \leq X \leq 35) = ? \]#### b. Percentage of Mothers Less Than 30 Years OldTo find out what percent of these mothers are less than 30 years old:\[ P(X < 30) = ? \]#### c. Percentage of Mothers More Than 33 Years OldTo find out what percent of these mothers are more than 33 years old:\[ P(X > 33) = ? \]The calculations for these percentages require the use of the Z-score formula and standard normal distribution tables or software.##### Z-score CalculationThe Z-score is calculated using the formula:\[ Z = \frac{X - \mu}{\sigma} \]Where:- $ X $ = value- $ \mu $ = mean- $ \sigma $ = standard deviationFor each specific question:- **Question a**: Compute Z-scores for X = 30 and X = 35 and find the area between them from the standard normal distribution table.- **Question b**: Compute Z-score for X = 30 and find the area to the left of this value.- **Question c**: Compute Z-score for X = 33 and find the area to the right of this value.These computations will help determine the required percentages based on the provided normal distribution parameters.

Let X denote the ages of multiple-birth mothers. Given that X follows N(mean = 31.7, SD = 5.2), then…

Answered: What percent of these mothers are…

What percent of these mothers are between the ages 30 to 35. What percent of these mothers are less than 30 years old. What percent of these mothers are more than 33 years old.

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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.

Question

Can you please answer this question and all of the sub problems and show all of the steps to the solution

### Statistical Analysis of Ages of Multiple-Birth Mothers

Consider the scenario where the ages of mothers giving birth to multiple babies (three or more) are normally distributed. According to the given data:

- **Mean Age**: 31.7 years
- **Standard Deviation**: 5.2 years

Based on this distribution, we can answer the following questions:

#### a. Percentage of Mothers Between Ages 30 to 35
To find out what percent of these mothers are between the ages of 30 and 35:

\[ P(30 \leq X \leq 35) = ? \]

#### b. Percentage of Mothers Less Than 30 Years Old
To find out what percent of these mothers are less than 30 years old:

\[ P(X < 30) = ? \]

#### c. Percentage of Mothers More Than 33 Years Old
To find out what percent of these mothers are more than 33 years old:

\[ P(X > 33) = ? \]

The calculations for these percentages require the use of the Z-score formula and standard normal distribution tables or software.

##### Z-score Calculation
The Z-score is calculated using the formula:

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

Where:
- $ X $ = value
- $ \mu $ = mean
- $ \sigma $ = standard deviation

For each specific question:
- **Question a**: Compute Z-scores for X = 30 and X = 35 and find the area between them from the standard normal distribution table.
- **Question b**: Compute Z-score for X = 30 and find the area to the left of this value.
- **Question c**: Compute Z-score for X = 33 and find the area to the right of this value.

These computations will help determine the required percentages based on the provided normal distribution parameters.

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