The number of ounces of water a person drinks per day is normally distributed with a standard deviation of 15 ounces. If Sean drinks 88 ounces per day with a z- score of 1.6, what is the mean ounces of water a day that a person drinks? Submit
The number of ounces of water a person drinks per day is normally distributed with a standard deviation of 15 ounces. If Sean drinks 88 ounces per day with a z- score of 1.6, what is the mean ounces of water a day that a person drinks? Submit
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Probability and Statistics Review
#### Instructor: Jane Jackson
**Problem:**
The number of ounces of water a person drinks per day is normally distributed with a standard deviation of 15 ounces. If Sean drinks 88 ounces per day with a z-score of 1.6, what is the mean ounces of water a day that a person drinks?
_Answer:_ _______
**Explanation:**
To solve this problem, use the z-score formula:
\[ z = \frac{(X - \mu)}{\sigma} \]
Where:
- \( z \) is the z-score
- \( X \) is the value in question (88 ounces)
- \( \mu \) is the mean
- \( \sigma \) is the standard deviation (15 ounces)
Rearrange the formula to solve for the mean (\( \mu \)):
\[ \mu = X - z\sigma \]
Substitute in the known values:
\[ \mu = 88 - (1.6 \times 15) \]
\[ \mu = 88 - 24 \]
\[ \mu = 64 \]
So, the mean ounces of water a person drinks per day is 64 ounces.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F103fb792-b567-4744-a444-2b7a46ef5541%2F5804884e-da3d-495c-97aa-9308241e9e8f%2Fkk7tp8s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability and Statistics Review
#### Instructor: Jane Jackson
**Problem:**
The number of ounces of water a person drinks per day is normally distributed with a standard deviation of 15 ounces. If Sean drinks 88 ounces per day with a z-score of 1.6, what is the mean ounces of water a day that a person drinks?
_Answer:_ _______
**Explanation:**
To solve this problem, use the z-score formula:
\[ z = \frac{(X - \mu)}{\sigma} \]
Where:
- \( z \) is the z-score
- \( X \) is the value in question (88 ounces)
- \( \mu \) is the mean
- \( \sigma \) is the standard deviation (15 ounces)
Rearrange the formula to solve for the mean (\( \mu \)):
\[ \mu = X - z\sigma \]
Substitute in the known values:
\[ \mu = 88 - (1.6 \times 15) \]
\[ \mu = 88 - 24 \]
\[ \mu = 64 \]
So, the mean ounces of water a person drinks per day is 64 ounces.
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