An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 148 lb and a standard deviation of 27.5 lb. a. If a pilot is randomly selected, find the probability that his weight is between 140lb and 201lb. The probability is approximately 0.58750 (Round to four decimal places as needed.) b. If 36 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 201 lb. The probability is approximately??
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 148 lb and a standard deviation of 27.5 lb. a. If a pilot is randomly selected, find the probability that his weight is between 140lb and 201lb. The probability is approximately 0.58750 (Round to four decimal places as needed.) b. If 36 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 201 lb. The probability is approximately??
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
Concept explainers
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Question
100%
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 148 lb and a standard deviation of 27.5 lb.
a. If a pilot is randomly selected, find the probability that his weight is between 140lb and 201lb.
The probability is approximately
0.58750
(Round to four decimal places as needed.)b. If 36 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 201 lb.
The probability is approximately??
- [Page 2 of the standard normal distribution](#)
#### Problem Statements and Solutions
**a. Single Pilot Probability**
Determine the probability that the weight of a randomly selected pilot falls between 140 lb and 201 lb.
- **Solution:** The probability is approximately **0.5875**. (Ensure you round to four decimal places as needed.)
**b. Group of Pilots Probability**
Consider a scenario with 36 different pilots. Calculate the probability that their average weight is between 140 lb and 201 lb.
- **Solution:** The probability is approximately [missing in the image].
#### Explanation of Solution Process
In the solution pop-up:
- Your answer was listed as "- .5867", which may be incorrect.
- The correct probability is "0.5875 ± 0.0002".
- Acceptable answers range from "0.5873 ± 0.0002" to "0.5874 to 0.5875 ± 0.0002".
This exercise is an application of the normal distribution and probability calculations, emphasizing precision in rounding and understanding distributions in a practical engineering context.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48e6a7d0-38a2-4f0f-929f-c6198e406298%2F749706cd-6933-4852-88de-fa74b308cb14%2Fa8g4x8w_processed.png&w=3840&q=75)
Transcribed Image Text:### Redesigning an Ejection Seat for Pilots
An engineer is tasked with redesigning an ejection seat for an airplane. The seat is originally tailored for pilots weighing between 140 lb and 201 lb. However, the weight of the new population of pilots is normally distributed, with a mean weight of 148 lb and a standard deviation of 27.5 lb.
- **Resources for Reference:**
- [Page 1 of the standard normal distribution](#)
- [Page 2 of the standard normal distribution](#)
#### Problem Statements and Solutions
**a. Single Pilot Probability**
Determine the probability that the weight of a randomly selected pilot falls between 140 lb and 201 lb.
- **Solution:** The probability is approximately **0.5875**. (Ensure you round to four decimal places as needed.)
**b. Group of Pilots Probability**
Consider a scenario with 36 different pilots. Calculate the probability that their average weight is between 140 lb and 201 lb.
- **Solution:** The probability is approximately [missing in the image].
#### Explanation of Solution Process
In the solution pop-up:
- Your answer was listed as "- .5867", which may be incorrect.
- The correct probability is "0.5875 ± 0.0002".
- Acceptable answers range from "0.5873 ± 0.0002" to "0.5874 to 0.5875 ± 0.0002".
This exercise is an application of the normal distribution and probability calculations, emphasizing precision in rounding and understanding distributions in a practical engineering context.
![An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 148 lb and a standard deviation of 27.5 lb.
Click here to view page 1 of the standard normal distribution.
Click here to view page 2 of the standard normal distribution.
a. If a pilot is randomly selected, find the probability that his weight is between 140 lb and 201 lb.
The probability is approximately **0.5875**. (Round to four decimal places as needed.)
b. If 36 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 201 lb.
The probability is approximately **[Blank]**. (Round to four decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48e6a7d0-38a2-4f0f-929f-c6198e406298%2F749706cd-6933-4852-88de-fa74b308cb14%2F4gtz14v_processed.png&w=3840&q=75)
Transcribed Image Text:An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 148 lb and a standard deviation of 27.5 lb.
Click here to view page 1 of the standard normal distribution.
Click here to view page 2 of the standard normal distribution.
a. If a pilot is randomly selected, find the probability that his weight is between 140 lb and 201 lb.
The probability is approximately **0.5875**. (Round to four decimal places as needed.)
b. If 36 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 201 lb.
The probability is approximately **[Blank]**. (Round to four decimal places as needed.)
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 24 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.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