Question

A ccmmon es ruqurement stat an envronment must fi the rar o people who all toween ne percent e or women a th In a thn knen Males have sittina knge hni hls lhat arn normally dístnbulted with a mnan n 21.4 nAnd standard te ton of e e ว่า percen e or men n des r an assembly war atle the sıttir knee he n must e con acer d which s te t stance ram he bc tomo e eel to 3 n Famalas t ดw: sitting kna haia hts that ara n all dist ihund with a mean a 19.1 n and a standard deviation n 1.2 in se this infor alian n ลก thR what is the minimum tatle dearance reqJred to salisay lhe requirement of fitting 95% of men? in (Round to one decimal place as needed.) Delermıne if the follow ng statement is true or false. If there dearance for 95% of males there will certainly ve clearance for al women in the DCeln 5%. OA. The statement is true because he 95th percentile for men ie greater than the 5th percentile for women O B、 The statement is felse because some women wil have eiting knee heights that are ouliers O C. The statement is true because some women will have sitting knee heights that ere outliers. Ο D· The steementis felse because the g5th percentile for men is greater than the 5th percentile ror women. The author is witing this exercise et a table with a dearance f 23,7 in, above the oor, vhat parcentege of men fit this table? Round to tao decima places 8s needed What parcentege of women fit this table? 1 1% (Rourd io two decima places as needed. Does the table appear to be made to fit amast everyoe? Choase te correct answer below. 0 A. The table wil fit ony 4%, of men. ○ B. c. D. The table wil only fit 1% of women. The table wil fit alm asl everyone except about 4% of men wtn the largest sitting knee heights. Not orough information to determine f the iable appears l) be mace ic ft almost everyone. lick to select your answer

Answer 1

For Men

Mean sitting Height (x₁) = 21.4 in

Std Deviation (s₁) = 1.3 in

Alpha = 0.05, Z_Critical = 1.96

95% CI = Mean +/- Z_Critical * Std Deviation = 21.4 +/- 1.96*1.3 = {18.9,23.9}

For Women

Mean sitting Height (x₂) = 19.1 in

Std Deviation (s₂) = 1.2 in

Alpha = 0.05, Z_Critical = 1.96

95% CI = Mean +/- Z_Critical * Std Deviation = 21.4 +/- 1.96*1.3 = {16.7,21.5}

a)

Minimum Table clearance for 95% Men = 18.9 in

b)

Option D

False.

c)

Z = (23.7-21.4)/1.3 = 1.77

P(X<=23.7) = P(z<1.77) = 0.9616 or 96.16%

d)

Z = (23.7-19.1)/1.2 = 3.83

P(X<=23.7) = P(z<3.83) = 0.999936 or ~100%

e)

Option C