Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=217 days and standard deviation Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) What is the probability that a randomly selected pregnancy lasts less than 211 days? The probability that a randomly selected pregnancy lasts less than 211 days is approximately 0.3621. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) O A. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last more than 211 days.
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=217 days and standard deviation Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) What is the probability that a randomly selected pregnancy lasts less than 211 days? The probability that a randomly selected pregnancy lasts less than 211 days is approximately 0.3621. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. (Round to the nearest integer as needed.) O A. If 100 pregnant individuals were selected independently from this population, we would expect pregnancies to last more than 211 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
![### Probability of Pregnancy Duration in Animals
The lengths of pregnancies for a certain animal are approximately normally distributed with a mean (μ) of 217 days and a standard deviation (σ) of 17 days. The calculations and interpretations provided below are derived from this data set.
#### (a) Probability That Pregnancy Lasts Less Than 211 Days
To determine the probability that a randomly selected pregnancy from this distribution lasts less than 211 days, we use the normal distribution parameters provided:
- **Mean (μ):** 217 days
- **Standard Deviation (σ):** 17 days
Using a standard normal distribution table or a calculator, the probability (P) that a pregnancy lasts less than 211 days is:
\[ P(X < 211) \approx 0.3621 \]
This probability is rounded to four decimal places as required.
Interpret this probability in the context given. Choose the most accurate statement and fill in the blank:
- **Option A:**
- If 100 pregnant individuals were selected independently from this population, we would expect \( \underline{\phantom{000}} \) pregnancies to last more than 211 days.
- **Option B:**
- If 100 pregnant individuals were selected independently from this population, we would expect \( 36 \) pregnancies to last less than 211 days.
- **Option C (Correct Selection):**
- If 100 pregnant individuals were selected independently from this population, we would expect \( \underline{\phantom{000}} \) pregnancies to last exactly 211 days.
In this case:
\[ \text{Number of pregnancies expected to last less than 211 days} \approx 0.3621 \times 100 = 36 (\text{rounded to nearest integer}) \]
Thus, the correct answer is option B:
- **Option B:**
- If 100 pregnant individuals were selected independently from this population, we would expect 36 pregnancies to last less than 211 days.
This probability and interpretation would aid in understanding and predicting the expected number of pregnancies falling below a certain number of days, given the distribution parameters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9885b298-0da3-45d1-bdbe-d5991ebff07e%2F612bc3c5-c815-46a4-bde4-a8bb5c325742%2Fi3dne9d_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability of Pregnancy Duration in Animals
The lengths of pregnancies for a certain animal are approximately normally distributed with a mean (μ) of 217 days and a standard deviation (σ) of 17 days. The calculations and interpretations provided below are derived from this data set.
#### (a) Probability That Pregnancy Lasts Less Than 211 Days
To determine the probability that a randomly selected pregnancy from this distribution lasts less than 211 days, we use the normal distribution parameters provided:
- **Mean (μ):** 217 days
- **Standard Deviation (σ):** 17 days
Using a standard normal distribution table or a calculator, the probability (P) that a pregnancy lasts less than 211 days is:
\[ P(X < 211) \approx 0.3621 \]
This probability is rounded to four decimal places as required.
Interpret this probability in the context given. Choose the most accurate statement and fill in the blank:
- **Option A:**
- If 100 pregnant individuals were selected independently from this population, we would expect \( \underline{\phantom{000}} \) pregnancies to last more than 211 days.
- **Option B:**
- If 100 pregnant individuals were selected independently from this population, we would expect \( 36 \) pregnancies to last less than 211 days.
- **Option C (Correct Selection):**
- If 100 pregnant individuals were selected independently from this population, we would expect \( \underline{\phantom{000}} \) pregnancies to last exactly 211 days.
In this case:
\[ \text{Number of pregnancies expected to last less than 211 days} \approx 0.3621 \times 100 = 36 (\text{rounded to nearest integer}) \]
Thus, the correct answer is option B:
- **Option B:**
- If 100 pregnant individuals were selected independently from this population, we would expect 36 pregnancies to last less than 211 days.
This probability and interpretation would aid in understanding and predicting the expected number of pregnancies falling below a certain number of days, given the distribution parameters.
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 3 steps
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