Assume that blood pressure readings are normally distributed with a mean of 115 and a standard deviation of 4.8. If 32 people are randomly selected, find the probability that their mean blood pressure will be less than 117. 00.8193 O 0.9908 O 0.0092 O 0.6615
Assume that blood pressure readings are normally distributed with a mean of 115 and a standard deviation of 4.8. If 32 people are randomly selected, find the probability that their mean blood pressure will be less than 117. 00.8193 O 0.9908 O 0.0092 O 0.6615
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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![**Question:**
Assume that blood pressure readings are normally distributed with a mean of 115 and a standard deviation of 4.8. If 32 people are randomly selected, find the probability that their mean blood pressure will be less than 117.
**Options:**
- A) 0.8193
- B) 0.9908
- C) 0.0092
- D) 0.6615
**Explanation:**
This is a problem involving the normal distribution. To find the probability that the mean blood pressure of 32 people is less than 117, you can use the concept of the sampling distribution of the sample mean, which also follows a normal distribution.
1. **Calculate the Standard Error (SE):**
\[
SE = \frac{\sigma}{\sqrt{n}} = \frac{4.8}{\sqrt{32}}
\]
2. **Find the Z-score:**
\[
Z = \frac{\bar{X} - \mu}{SE} = \frac{117 - 115}{SE}
\]
3. **Use the Z-score to find the probability from standard normal distribution tables or computational tools.**
Remember, this assumes a normal distribution where various statistical methods can easily determine probabilities. Adjust calculations to apply to specific statistical software or manual calculations using a Z-table for precision.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe930625e-c503-4d73-983b-5bd5cd1a3834%2F26a12f97-95d2-41ab-8f57-76e7d739fa74%2Fcv2y5si_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Assume that blood pressure readings are normally distributed with a mean of 115 and a standard deviation of 4.8. If 32 people are randomly selected, find the probability that their mean blood pressure will be less than 117.
**Options:**
- A) 0.8193
- B) 0.9908
- C) 0.0092
- D) 0.6615
**Explanation:**
This is a problem involving the normal distribution. To find the probability that the mean blood pressure of 32 people is less than 117, you can use the concept of the sampling distribution of the sample mean, which also follows a normal distribution.
1. **Calculate the Standard Error (SE):**
\[
SE = \frac{\sigma}{\sqrt{n}} = \frac{4.8}{\sqrt{32}}
\]
2. **Find the Z-score:**
\[
Z = \frac{\bar{X} - \mu}{SE} = \frac{117 - 115}{SE}
\]
3. **Use the Z-score to find the probability from standard normal distribution tables or computational tools.**
Remember, this assumes a normal distribution where various statistical methods can easily determine probabilities. Adjust calculations to apply to specific statistical software or manual calculations using a Z-table for precision.
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