Question

Engineers want to design seats in commercial aircraft so that they are wide enough to fit​ 99% of all adults.​ (accommodating 100% of adults would require very wide seats that would be much too​ expensive.) assume adults have hip widths that are normally distributed with a mean of in. and a standard deviation of in. find p99. that​ is, find the hip width for adults that separates the smallest​ 99% from the largest​ 1%.

Answer 1

Airlines and engineers can use Z-scores to determine the ideal seat width to accommodate 99% of adults by applying statistical methods involving normal distribution.

Step-by-step explanation:

To answer the question about designing airplane seats to fit 99% of adults, one must use the concept of the normal distribution from statistics. The 99th percentile (P99) can be found using the Z-score formula: Z = (X - μ) / σ, where X is the value that corresponds to P99, μ is the mean hip width, and σ is the standard deviation. Having the Z-score that corresponds to the 99th percentile, one can then solve for X, which will provide the hip width that separates the smallest 99% of adults from the largest 1%.