Question

6.2.19-E Question Help Suppose that the sitting back-to-knee lenge for a group of adults as a nomal distribution with a mean of 24.4 in and a standard deviation of 11 in These data are often used in the design of different seats Induding wirerat a train seats, theater seats, and classroom seats. Instead of using 0.05 for identifying significant values, use the criteria that a value is significantly high if Pix or greater 01 and a valves significanty low Pix or less)0.01. Find the back to knee lengths separating significant values from those that are not significant Using these reria, is a back-to knee length of 26.7 in significantly high? Find the back okrelengths separating significant values from those that are not significant Back to the length greater than in and (Round to one decimal place as needed.) than in are not significant, and values outside that range are considered significant

Answer 1

solna we have X: Back-to-knee length of adults. giren e r - 24.14 in 0: 1 in we have value of x is significantly high it PCX or greater) sool and signioi -cantly low if P(x or less.) soola omrony obmota • consider X=k for which dot PCK < x = 0.01 hence length greater be significantly high. : PCK & x) so.ol- than k will It ie P(x-re ex-re) r (z-score = x-M ~ N(0,1)) plk-24.4 & 2) = 0.01

ie Plz < K-24.4 > 1-0.01 Plz<K-24.4 70.991 from standar normal probability table we get value of 2-score as 2 = 2.33 - k-24.4 - 2.33 K = 233 * tot + 24.4 K = 26.963 hence value high if it is of x will be significantly greater than 26.963 Similarly consider u I such value no x less than 'l' -cantly low or . P ( x < 1 ) = .0.01 with that is signiti- - P(x-4 < 1-4) & 0.1
Summary : The lengths of back-to-knee between 21.8837 and 26.936 are not significant.