if the mean height of an indian police inspector be 170 cm with variance 25 cm square.how many inspectors out of 1000 would you expect between 170cm and 180 cm. find its solution
Answers
Given : the mean height of an Indian police inspector be 170 cm with variance 25 cm square.
To Find : how many inspectors out of 1000 would you expect between 170cm and 180 cm.
Solution:
mean height = 70 cm
variance 25 cm²
variance = SD² = 25
=> SD = 5 cm
Z score = ( Value - Mean) /SD
between 170cm and 180 cm.
Z score for 170 = ( 170 - 170) / 5 = 0 => 50 % below 170 cm height
Z score for 180 = ( 180 - 170) / 5 = 2 => 97.72 % below 180 cm height
Hence 97.72 - 50 = 47.72 % between 170cm and 180 cm
Total = 1000
Hence 1000 * 47.72 % = 477.2 ≈ 477
Hence 477 inspectors between 170cm and 180 cm height
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