It is known that the heights of adult males of a certain township are normally distributed with average height as 171.25cm with standard deviation 9.5cm. How many adult males in a random sample of 1000 from this township would you expect to have the height (i) more than 180cm and (ii) less than 150cm?
Answers
Given : males of a certain township are normally distributed with average height as 171.25cm with standard deviation 9.5cm.
To Find : in a random sample of 1000 height
(i) more than 180cm
(ii) less than 150cm
Solution:
Mean = 171.25 cm
SD = 9.5 cm
Z score = ( Value - Mean)/SD
more than 180cm
Value = 180
=> z score = ( 180 - 171.25)/9.5 = 0.921
z score 0.921 means 82.15 % upto 180 cm
more than 180cm = 100 - 82.15 = 17.85 %
=> out of 1000 = (17.85/100)*1000 = 178.5 = 179
Less than 150 cm
Value = 150
=> z score = ( 150 - 171.25)/9.5 = -2.237
z score-2.237 means 1.26 % upto 150 cm
Less than 150 cm
=> out of 1000 = (1.26/100)*1000 = 12.6 = 13
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