Suppose that human pulse rates for children over 10 and adults are approximately normally distributed with a mean of 78 and standard deviation of 12. Suppose as random.Answer the question following question, rounding your answers to 4 decimal places. ### Understanding Human Pulse Rate ProbabilitiesLet's explore the given scenario where human pulse rates for children over 10 and adults are approximately normally distributed. The pulse rates have a mean of 78 and a standard deviation of 12. Given this distribution, we can answer some specific probability questions about an individual's pulse rate.#### Important Concepts:- **Normal Distribution:** A type of continuous probability distribution for a real-valued random variable.- **Mean (μ):** The average of all data points, here it is 78.- **Standard Deviation (σ):** Measurement of the amount of variation or dispersion, in this case, it is 12.- **Z-score:** A statistical measurement that describes a value's relationship to the mean of a group of values.#### Questions and Solutions:Make sure to round your answers to 4 decimal places.1. **The probability that the pulse rate of the individual is less than 60:**\[ P(X < 60) = \boxed{1.83} \]2. **The probability that the pulse rate of the individual is more than 100:**\[ P(X > 100) = \boxed{0.8996} \]3. **The probability that the pulse rate of the individual is between 60 and 80:**\[ P(60 < X < 80) = \boxed{} \]4. **The probability that the pulse rate of the individual is either less than 55 or more than 95:**\[ P(X < 55 \text{ or } X > 95) = \boxed{97.74} \]### Detailed Explanation for Each Probability:1. **Less than 60:** - Convert the pulse rate to a z-score: $ Z = \frac{X - \mu}{\sigma} = \frac{60 - 78}{12} = -1.5 $. - Use a Z-table to find the probability corresponding to $ Z = -1.5 $.2. **More than 100:** - Convert the pulse rate to a z-score: $ Z = \frac{100 - 78}{12} = 1.8333 $. - Use a Z-table to find the probability corresponding to $ Z = 1.8333 $.3. **Between 60 and 80:** - Find the z-score for 60 and 80

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Answered: Suppose that human pulse rates for…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that human pulse rates for children over 10 and adults are approximately normally distributed with a mean of 78 and standard deviation of 12. Suppose as random.Answer the question following question, rounding your answers to 4 decimal places.

### Understanding Human Pulse Rate Probabilities

Let's explore the given scenario where human pulse rates for children over 10 and adults are approximately normally distributed. The pulse rates have a mean of 78 and a standard deviation of 12. Given this distribution, we can answer some specific probability questions about an individual's pulse rate.

#### Important Concepts:
- **Normal Distribution:** A type of continuous probability distribution for a real-valued random variable.
- **Mean (μ):** The average of all data points, here it is 78.
- **Standard Deviation (σ):** Measurement of the amount of variation or dispersion, in this case, it is 12.
- **Z-score:** A statistical measurement that describes a value's relationship to the mean of a group of values.

#### Questions and Solutions:
Make sure to round your answers to 4 decimal places.

1. **The probability that the pulse rate of the individual is less than 60:**

\[ P(X < 60) = \boxed{1.83} \]

2. **The probability that the pulse rate of the individual is more than 100:**

\[ P(X > 100) = \boxed{0.8996} \]

3. **The probability that the pulse rate of the individual is between 60 and 80:**

\[ P(60 < X < 80) = \boxed{} \]

4. **The probability that the pulse rate of the individual is either less than 55 or more than 95:**

\[ P(X < 55 \text{ or } X > 95) = \boxed{97.74} \]

### Detailed Explanation for Each Probability:

1. **Less than 60:**
- Convert the pulse rate to a z-score: $ Z = \frac{X - \mu}{\sigma} = \frac{60 - 78}{12} = -1.5 $.
- Use a Z-table to find the probability corresponding to $ Z = -1.5 $.

2. **More than 100:**
- Convert the pulse rate to a z-score: $ Z = \frac{100 - 78}{12} = 1.8333 $.
- Use a Z-table to find the probability corresponding to $ Z = 1.8333 $.

3. **Between 60 and 80:**
- Find the z-score for 60 and 80

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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