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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### 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.
Transcribed Image Text:### 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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