If an individual is selected, find the probability that the individual's pressure will be between 118.4 and 121.9 mmHg. P(118.4 < X < 121.9) = 0.2472 Part: 1/3 Part 2 of 3 If a sample of 28 adults is randomly selected, find the probability that the sample mean will be between 118.4 and 121.9 mmHg. Assume that the sample is taken from a large population and the correction factor can be ignored. P(118.4 < X < 121.9) = X

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
### Systolic Blood Pressure Analysis

**Overview:** 
Consider a mean systolic blood pressure of normal adults recorded as 120 millimeters of mercury (mmHg), with a standard deviation of 5.6. The variable is considered normally distributed. Calculations should be rounded to at least four decimal places, with intermediate z-value calculations precise to two decimal places.

#### Part 1 of 3:
- **Probability Calculation for an Individual:**
  Determine the probability that an individual's systolic blood pressure is between 118.4 mmHg and 121.9 mmHg.

  \[
  P(118.4 < X < 121.9) = 0.2472
  \]

  This indicates that there is a 24.72% probability for an individual's pressure to fall within this specified range.

#### Part 2 of 3:
- **Probability Calculation for a Sample Mean:**
  Consider a randomly selected sample of 28 adults. Find the probability that the sample mean blood pressure is between 118.4 mmHg and 121.9 mmHg. Assume the correction factor is negligible since the sample is from a large population.

  \[
  P(118.4 < \overline{X} < 121.9) = \,?
  \]

  Calculations here involve determining the z-score for the sample mean and applying the central limit theorem, which modifies the standard deviation for the sample. This step requires solving for the probability with given parameters for better statistical inference. 

**Progress Indicator:**
- Part 1 is completed as denoted by the [✓] checkmark and the progress bar showing completion of the first segment out of three. 

This breakdown helps users understand the statistical methods used for calculating probabilities related to systolic blood pressure in both individual cases and sample means.
Transcribed Image Text:### Systolic Blood Pressure Analysis **Overview:** Consider a mean systolic blood pressure of normal adults recorded as 120 millimeters of mercury (mmHg), with a standard deviation of 5.6. The variable is considered normally distributed. Calculations should be rounded to at least four decimal places, with intermediate z-value calculations precise to two decimal places. #### Part 1 of 3: - **Probability Calculation for an Individual:** Determine the probability that an individual's systolic blood pressure is between 118.4 mmHg and 121.9 mmHg. \[ P(118.4 < X < 121.9) = 0.2472 \] This indicates that there is a 24.72% probability for an individual's pressure to fall within this specified range. #### Part 2 of 3: - **Probability Calculation for a Sample Mean:** Consider a randomly selected sample of 28 adults. Find the probability that the sample mean blood pressure is between 118.4 mmHg and 121.9 mmHg. Assume the correction factor is negligible since the sample is from a large population. \[ P(118.4 < \overline{X} < 121.9) = \,? \] Calculations here involve determining the z-score for the sample mean and applying the central limit theorem, which modifies the standard deviation for the sample. This step requires solving for the probability with given parameters for better statistical inference. **Progress Indicator:** - Part 1 is completed as denoted by the [✓] checkmark and the progress bar showing completion of the first segment out of three. This breakdown helps users understand the statistical methods used for calculating probabilities related to systolic blood pressure in both individual cases and sample means.
Expert Solution
Step 1: given information

Mean=mu=120

Standard deviation =5.6

steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman