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The height measurements of 600 adult males are arranged in ascending order and it is observed that 180th and 450th entries are 46.3 and 67.8 inch respectively. If the measurements are normally distributed.
i. Find the mean and the standard deviation of the distribution.
ii. Find the number of males whose height is between 40 and 70 inches.
Answers
Given : The height measurements of 600 adult males are arranged in ascending order and it is observed that 180th and 450th entries are 46.3 and 67.8 inch respectively. the measurements are normally distributed.
To find : i. Find the mean and the standard deviation of the distribution.
ii. Find the number of males whose height is between 40 and 70 inches.
Solution:
Total 600
Z score = ( Value - Mean)/SD
180 people = (180/600) * 100 = 30%
z score for 30% = -0.525
=> -0.525 = (46.3 - Mean)/SD
=> 46.3 - Mean = -0.525SD
450 people mean = (450/600) * 100 = 75%
z score for 75% = 0.675
=> 0.675 = (67.8 - Mean)/SD
=> 67.8 - Mean = 0.675SD
=> 21.5 = 1.2SD
> SD = 17.9
=>Mean = 55.7
Height between 40 & 70
Z score for 40 = ( 40 - 55.7)/17.9 = -0.877 => 19 % below this
Z score for 70 = ( 70 - 55.7)/17.9 = 0.799 => 78.8 % below this
Between 40 & 70 = 78.8 - 19 = 59.8 %
= (59.8/100) * 600
= 359
359 Males whose height is between 40 & 70 inches
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SD = 17.9
Mean = 55.7
Number of males of height between 40 and 70 inches = 359
Step-by-step explanation:
Given : The height measurements of 600 adult males are arranged in ascending order and it is observed that 180th and 450th entries are 46.3 and 67.8 inch respectively. The measurements are normally distributed.
Find :
Mean and standard deviation of the distribution.
Number of males whose height is between 40 and 70 inches.
Solution:
Total = 600
Z score = (Value - Mean)/SD
% of total for 180 people = (180/600) * 100 = 30%
z score for 30% = -0.525
-0.525 = (46.3 - Mean)/SD
46.3 - Mean = -0.525 * SD
% of total for 450 people = (450/600) * 100 = 75%
z score for 75% = 0.675
0.675 = (67.8 - Mean)/SD
67.8 - Mean = 0.675 * SD
21.5 = 1.2 * SD
SD = 17.9
Mean = 55.7
Z score for 40 = (40 - 55.7) / 17.9 = -0.877 => 19 % below this
Z score for 70 = (70 - 55.7) / 17.9 = 0.799 => 78.8 % below this
Between 40 & 70 inches = 78.8 - 19 = 59.8 %
= (59.8/100) * 600
= 359
Number of males of height between 40 and 70 inches = 359