We appreciate your visit to An engineer is planning to redesign an ejection seat for an airplane The seat was designed for pilots weighing between 140 and 181 pounds The. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The question deals with calculating probabilities using the concept of normal distribution and z-scores. The probability of a pilot's weight being between 140 and 187 pounds is approximately 55.05%
Explanation:
The subject of this question pertains to statistics, particularly normal distribution and probabilities. The problem involves an engineer redesigning an ejection seat for an airplane and needing to account for the weights of pilots, which follow a normal distribution with a mean of 150 pounds and a standard deviation of 27.7 pounds. We are asked to find the probability of a pilot's weight falling between 140 and 187 pounds.
To find this, we need to convert the individual weights to z-scores, which is a measure of how many standard deviations an element is from the mean. After which, we need to look these up in a standard normal distribution table to find the probabilities. The formula used for finding the z-score is: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
For 140: Z1 = (140 - 150) / 27.7 = -0.36. And for 187: Z2 = (187 - 150) / 27.7 = 1.34. Using a standard normal distribution table, we find that the probabilities associated with these z-scores are approximately 0.3594 and 0.9099, respectively. Subtracting these gives us 0.5505 or 55.05% as the probability that the selected pilot's weight falls between 140 and 187 pounds.
Learn more about Normal Distribution here:
https://brainly.com/question/30390016
#SPJ11
Thanks for taking the time to read An engineer is planning to redesign an ejection seat for an airplane The seat was designed for pilots weighing between 140 and 181 pounds The. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
