The duration of gestation in healthy humans is approximately normally distributed with a mean of 280 days and a standard deviation of 10 days. A certain obstetrician has 200 "expecting" patients. How many should he expect to give birth in less than 265 days ?
The duration of gestation in healthy humans is approximately normally distributed with a mean of 280 days and a standard deviation of 10 days. A certain obstetrician has 200 "expecting" patients. How many should he expect to give birth in less than 265 days ?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Just write it out. Please write in print or text. I can’t understand cruise
![**Question 8: Understanding Normal Distribution in Human Gestation**
The duration of gestation in healthy humans is approximately normally distributed with a mean of 280 days and a standard deviation of 10 days. If an obstetrician has 200 "expecting" patients, how many should he expect to give birth in less than 265 days?
**Analysis:**
To solve this problem, we need to understand how normal distribution works. In a normal distribution:
- The mean (average) is 280 days.
- The standard deviation (a measure of how spread out numbers are) is 10 days.
We are asked to find the number of patients who are expected to give birth in less than 265 days. This requires calculating the probability of a gestation period being less than 265 days and then applying that probability to the total number of patients.
**Calculation Steps**:
1. **Determine the Z-score**: The Z-score tells us how many standard deviations a particular value is from the mean.
\[
Z = \frac{X - \mu}{\sigma}
\]
Where:
- \(X\) is the value for which we are finding the Z-score (265 days).
- \(\mu\) is the mean (280 days).
- \(\sigma\) is the standard deviation (10 days).
\[
Z = \frac{265 - 280}{10} = \frac{-15}{10} = -1.5
\]
2. **Find the Probability**: Using the Z-score, we can find the probability by looking up -1.5 in the standard normal distribution table, or using a calculator.
Approximately \(P(Z < -1.5) = 0.0668\).
3. **Calculate the Expected Number of Patients**: Multiply the probability by the total number of patients.
\[
\text{Number of patients} = 0.0668 \times 200 = 13.36
\]
Since the number of patients cannot be a fraction, the obstetrician can expect about 13 patients to give birth in less than 265 days.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d390e3f-8275-41b8-b687-67a83e0a6b78%2F44ee3db4-b1ac-42a3-8729-1a97ba6690c7%2F3w1b24_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 8: Understanding Normal Distribution in Human Gestation**
The duration of gestation in healthy humans is approximately normally distributed with a mean of 280 days and a standard deviation of 10 days. If an obstetrician has 200 "expecting" patients, how many should he expect to give birth in less than 265 days?
**Analysis:**
To solve this problem, we need to understand how normal distribution works. In a normal distribution:
- The mean (average) is 280 days.
- The standard deviation (a measure of how spread out numbers are) is 10 days.
We are asked to find the number of patients who are expected to give birth in less than 265 days. This requires calculating the probability of a gestation period being less than 265 days and then applying that probability to the total number of patients.
**Calculation Steps**:
1. **Determine the Z-score**: The Z-score tells us how many standard deviations a particular value is from the mean.
\[
Z = \frac{X - \mu}{\sigma}
\]
Where:
- \(X\) is the value for which we are finding the Z-score (265 days).
- \(\mu\) is the mean (280 days).
- \(\sigma\) is the standard deviation (10 days).
\[
Z = \frac{265 - 280}{10} = \frac{-15}{10} = -1.5
\]
2. **Find the Probability**: Using the Z-score, we can find the probability by looking up -1.5 in the standard normal distribution table, or using a calculator.
Approximately \(P(Z < -1.5) = 0.0668\).
3. **Calculate the Expected Number of Patients**: Multiply the probability by the total number of patients.
\[
\text{Number of patients} = 0.0668 \times 200 = 13.36
\]
Since the number of patients cannot be a fraction, the obstetrician can expect about 13 patients to give birth in less than 265 days.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman