Assuming that height data on a valid sample of NNS employees was collected and a
ID: 3152149 • Letter: A
Question
Assuming that height data on a valid sample of NNS employees was collected and analyzed, producing the following : Average = 5' 8" Standard Deviation = 4" Calculate: Height range (centered around the mean) that would include 68% of the shipyard employees? Height of a doorway that will allow 90% of employees to walk under? Height of a doorway that will cause 3% of employees to hit their heads? Percent of employees who would hit their head on 5' 10" doorway? Percent of employees between 5'2" and 5'9"?Explanation / Answer
a) According to emperical rule, 68% of data will fall under 1 standard deviations from the mean.
Height range is 68'' +1*4''=72'' [5'8''=5*12+8''=68'']
b) Z score =1.65, Xbar=68'', sd=4'', compute Xi
1.65=(Xi-68)/4
Xi=74.6''
c) According to emperical rule, 99.7% of scores fall within 3 standard deviations from mean.
Required height: 68-3*4=56''
d) Xi=70'', s=4'', Xbar=68'', compute z score.
Z=(70-68)/4=0.5
P(X>5'10'')=P(Z>0.5)=0.3085~30.85%
e) Compute z csore, corresponding to 62'' and 69''
Z1=(62-68)/4=-1.5 Z2=(69-68)/4=0.25
P(5'2''<X<5'9'')=0.4332+0.0987=0.5319~53.19%