Systolic blood pressure for a group of women is normally distributed, with a mean of 115 and a standard deviation of 12. Find the probability that a woman selected at random has the following blood pressures. (Round your answers to four decimal places.)(a) greater than 135(b) less than 105(c) between 105 and 125 ## Areas Under the Standard Normal CurveThis table provides the area under the standard normal curve between $ z = 0 $ and $ z = z_0 $ for $ z_0 \geq 0 $. It is important for finding probabilities related to normal distributions. Areas for negative values of $ z_0 $ are obtained by symmetry.### Explanation of the ChartThe chart is a table listing pairs of values $ z_0 $ and $ A $, where $ A $ represents the area under the curve.- **Columns in the table:** - **$ z_0 $**: The z-score, or the number of standard deviations from the mean. - **$ A $**: The area under the standard normal distribution curve from $ z = 0 $ to the specified $ z_0 $.- **Diagram:** - The curve at the top right shows a standard normal distribution with a mean $ \mu = 0 $ and standard deviation $ \sigma = 1 $. - The shaded area represents the area $ A $ from the mean to the specified $ z_0 $.### Sample Values from the Table- **$ z_0 = 0.00 $, $ A = 0.0000 $** indicates no area at $ z = 0 $.- **$ z_0 = 0.50 $, $ A = 0.1915 $** represents the area up to half a standard deviation.- **$ z_0 = 1.00 $, $ A = 0.3413 $** shows the area within one standard deviation from the mean.- **$ z_0 = 1.50 $, $ A = 0.4332 $** represents the area within one and a half standard deviations.This table is useful for finding the cumulative probabilities associated with specific z-scores, aiding in statistical calculations and assessments.

Given : μ = 115 σ = 12 a) PX > 135 = 1 - P X ≤ 135 PX > 135 = 1 - P X-11512 ≤ 135-11512 PX…

Answered: Systolic blood pressure for a group of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Systolic blood pressure for a group of women is normally distributed, with a mean of 115 and a standard deviation of 12. Find the probability that a woman selected at random has the following blood pressures. (Round your answers to four decimal places.)

(a) greater than 135

(b) less than 105

(c) between 105 and 125

## Areas Under the Standard Normal Curve

This table provides the area under the standard normal curve between $ z = 0 $ and $ z = z_0 $ for $ z_0 \geq 0 $. It is important for finding probabilities related to normal distributions. Areas for negative values of $ z_0 $ are obtained by symmetry.

### Explanation of the Chart

The chart is a table listing pairs of values $ z_0 $ and $ A $, where $ A $ represents the area under the curve.

- **Columns in the table:**
- **$ z_0 $**: The z-score, or the number of standard deviations from the mean.
- **$ A $**: The area under the standard normal distribution curve from $ z = 0 $ to the specified $ z_0 $.

- **Diagram:**
- The curve at the top right shows a standard normal distribution with a mean $ \mu = 0 $ and standard deviation $ \sigma = 1 $.
- The shaded area represents the area $ A $ from the mean to the specified $ z_0 $.

### Sample Values from the Table

- **$ z_0 = 0.00 $, $ A = 0.0000 $** indicates no area at $ z = 0 $.
- **$ z_0 = 0.50 $, $ A = 0.1915 $** represents the area up to half a standard deviation.
- **$ z_0 = 1.00 $, $ A = 0.3413 $** shows the area within one standard deviation from the mean.
- **$ z_0 = 1.50 $, $ A = 0.4332 $** represents the area within one and a half standard deviations.

This table is useful for finding the cumulative probabilities associated with specific z-scores, aiding in statistical calculations and assessments.

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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