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MATLAB: An Introduction with Applications
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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Assume that 21 year old woman’s heart rate at rest I normally distributed with a mean of 62 bpm and a standard deviation of 4 bpm. If 400 women are examined, how many would you expect to have a heart rate of less than 64? How many women out of 400 would you expect to have a heart rate of less than 64? (Type answer as a whole number)
**Section 14.4 – The Normal Distribution** The normal distribution (normal curve) is a way to study data using the information you have learned about. A normal distribution is a bell-shaped curve that is symmetric with respect to the mean. A normal distribution usually applies to a whole population, not a sample, therefore the mean is now called (μ, mu). **Graph/Diagram Explanation:** The image features a bell-shaped curve representing a normal distribution, which is symmetric about the mean (μ). The curve is divided into sections that indicate the percentage of the population that falls within certain ranges of standard deviations (σ) from the mean. 1. **Center Section (μ):** - The central section represents the mean (μ). 2. **First Standard Deviations (±1σ):** - The section within one standard deviation of the mean (μ ± 1σ) includes 68% of the data (34% on each side). 3. **Second Standard Deviations (±2σ):** - The section from one to two standard deviations away from the mean (μ ± 2σ) includes 27% of the data (13.5% on each side). 4. **Third Standard Deviations (±3σ):** - The section from two to three standard deviations away from the mean (μ ± 3σ) includes 4.7% of the data (2.35% on each side). 5. **Beyond Three Standard Deviations:** - The tails of the curve beyond three standard deviations from the mean include 0.3% of the data (0.15% on each side). Understanding the normal distribution is crucial for studying statistical data, as it helps in predicting probabilities and making inferences about a population. This section is foundational for further studies in statistics and data analysis.
Transcribed Image Text:**Section 14.4 – The Normal Distribution** The normal distribution (normal curve) is a way to study data using the information you have learned about. A normal distribution is a bell-shaped curve that is symmetric with respect to the mean. A normal distribution usually applies to a whole population, not a sample, therefore the mean is now called (μ, mu). **Graph/Diagram Explanation:** The image features a bell-shaped curve representing a normal distribution, which is symmetric about the mean (μ). The curve is divided into sections that indicate the percentage of the population that falls within certain ranges of standard deviations (σ) from the mean. 1. **Center Section (μ):** - The central section represents the mean (μ). 2. **First Standard Deviations (±1σ):** - The section within one standard deviation of the mean (μ ± 1σ) includes 68% of the data (34% on each side). 3. **Second Standard Deviations (±2σ):** - The section from one to two standard deviations away from the mean (μ ± 2σ) includes 27% of the data (13.5% on each side). 4. **Third Standard Deviations (±3σ):** - The section from two to three standard deviations away from the mean (μ ± 3σ) includes 4.7% of the data (2.35% on each side). 5. **Beyond Three Standard Deviations:** - The tails of the curve beyond three standard deviations from the mean include 0.3% of the data (0.15% on each side). Understanding the normal distribution is crucial for studying statistical data, as it helps in predicting probabilities and making inferences about a population. This section is foundational for further studies in statistics and data analysis.
**Standard Normal Distribution Table** The table below is a Standard Normal Distribution table, which displays cumulative probabilities for a standard normal distribution (Z-distribution). This table is essential for statistical analysis and for finding the probability that a standard normal random variable is less than or equal to a given value. **Using the Table:** 1. **Rows and Columns:** - The rows represent the first two digits and the first decimal place of the Z-value (e.g., 0.00, 0.01, 0.02, ..., 3.09). - The columns represent the second decimal place of the Z-value (e.g., 0.00, 0.01, 0.02, ..., 0.09). 2. **Finding the Probability:** - To find the cumulative probability of a Z-value, locate the row corresponding to the first two digits and the first decimal place of your Z-value. - Then, move across to the column corresponding to the second decimal place of your Z-value. - The cell where the row and column intersect gives the cumulative probability. **Example:** Suppose we want to find the cumulative probability for Z = 1.34: - Locate the row for 1.3. - Move across to the column for 0.04. - The intersection cell shows a cumulative probability of 0.9099. **Table Explanation:** The table is organized into 56 rows and 10 columns. Each cell represents the cumulative probability from 0.0 to 3.09 standard deviations. | Z-Value | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | |---------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------| | 0.00 | 0.000 | 0.040 | 0.080 | 0.120 | 0.160 | 0.200 | 0.240 | 0.280 | 0.320 | 0.360 | | 0.10 | 0.400 | 0.440 | 0.480 | 0.520 | 0.560 |
Transcribed Image Text:**Standard Normal Distribution Table** The table below is a Standard Normal Distribution table, which displays cumulative probabilities for a standard normal distribution (Z-distribution). This table is essential for statistical analysis and for finding the probability that a standard normal random variable is less than or equal to a given value. **Using the Table:** 1. **Rows and Columns:** - The rows represent the first two digits and the first decimal place of the Z-value (e.g., 0.00, 0.01, 0.02, ..., 3.09). - The columns represent the second decimal place of the Z-value (e.g., 0.00, 0.01, 0.02, ..., 0.09). 2. **Finding the Probability:** - To find the cumulative probability of a Z-value, locate the row corresponding to the first two digits and the first decimal place of your Z-value. - Then, move across to the column corresponding to the second decimal place of your Z-value. - The cell where the row and column intersect gives the cumulative probability. **Example:** Suppose we want to find the cumulative probability for Z = 1.34: - Locate the row for 1.3. - Move across to the column for 0.04. - The intersection cell shows a cumulative probability of 0.9099. **Table Explanation:** The table is organized into 56 rows and 10 columns. Each cell represents the cumulative probability from 0.0 to 3.09 standard deviations. | Z-Value | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | |---------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------| | 0.00 | 0.000 | 0.040 | 0.080 | 0.120 | 0.160 | 0.200 | 0.240 | 0.280 | 0.320 | 0.360 | | 0.10 | 0.400 | 0.440 | 0.480 | 0.520 | 0.560 |
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