An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 147 lb and a standard deviation of 28.9 lb. Pictures of Charts are attached for the standard normal distribution. a. If a pilot is randomly selected, find the probability that his weight is between 140lb and 191 lb. The probability is approximately? (Round to four decimal places as needed.) b. If 40 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 191lb. The probability is approximately (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? Choose one from below. A. Part (a) because the seat performance for a sample of pilots is more important. B. Part (b) because the seat performance for a sample of pilots is more important. C. Part (a) because the seat performance for a single pilot is more important. D. Part (b) because the seat performance for a single pilot is more important.
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 147 lb and a standard deviation of 28.9 lb. Pictures of Charts are attached for the standard normal distribution. a. If a pilot is randomly selected, find the probability that his weight is between 140lb and 191 lb. The probability is approximately? (Round to four decimal places as needed.) b. If 40 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 191lb. The probability is approximately (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? Choose one from below. A. Part (a) because the seat performance for a sample of pilots is more important. B. Part (b) because the seat performance for a sample of pilots is more important. C. Part (a) because the seat performance for a single pilot is more important. D. Part (b) because the seat performance for a single pilot is more important.
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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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
An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 140lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 147 lb
and a standard deviation of 28.9 lb.
and a standard deviation of 28.9 lb.
Pictures of Charts are attached for the standard normal distribution.
a. If a pilot is randomly selected, find the probability that his weight is between 140lb and 191 lb.
The probability is approximately?
(Round to four decimal places as needed.)
(Round to four decimal places as needed.)
b. If 40 different pilots are randomly selected, find the probability that their mean weight is between 140 lb and 191lb.
The probability is approximately
(Round to four decimal places as needed.)
(Round to four decimal places as needed.)
c. When redesigning the ejection seat, which probability is more relevant?
Choose one from below.
Part (a) because the seat performance for a sample of pilots is more important.
Part (b) because the seat performance for a sample of pilots is more important.
Part (a) because the seat performance for a single pilot is more important.
Part (b) because the seat performance for a single pilot is more important.
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0.07
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0.09
0.5
0.504
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0.512
0.516
0.5199
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0.67
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0.5
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0.7224
0.6
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0.8
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0.8315
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1.
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1.2
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1.3
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1.4
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1.5
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0.9429
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1.6
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1.7
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1.8
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1.9
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2.
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2.1
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2.2
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2.3
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2.4
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2.5
0.9938
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2.6
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2.7
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2.8
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2.9
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3
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3.4
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3.5 and up
0.9999
Transcribed Image Text:0.01
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0.4602
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0.5
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