2) (10 pts) A height study(X) is conducted for a group of normally distributed employees at a small company. The average height of the employees is 66 inches and the standard deviation is 4 inches.
Solution :
Given that,
mean = = 66
standard deviation = = 4
a ) P ( x > 67.5 )
= 1 - P (x < 67.5 )
= 1 - P ( x - / ) < ( 67.5 - 66 / 4)
= 1 - P ( z < 1.5 / 4 )
= 1 - P ( z < 0.375)
Using z table
= 1 - 0.6462
= 0.3538
Probability = 0.3538
b ) P ( 61 < x < 64.5 )
P ( 61 - 66 / 4) < ( x - / ) < ( 64.5 - 66 / 4)
P ( - 5 / 4 < z < -1.5 / 4 )
P (- 1.25 < z < - 0.375 )
P (z < - 0.375 ) - p ( z < - 1.25 )
Using z table
= 0.3538 - 0.1056
= 0.2482
Probability = 0.2482
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