A normal population has a mean of 61 and a standard deviation of 20. A. What proportion of the population is greater than 108? B. What is the probability that a randomly chosen valve will be less than 81?
Solution :
Given that,
mean = = 61
standard deviation = = 20
a ) P (x > 108 )
= 1 - P (x < 108 )
= 1 - P ( x - / ) < ( 108 - 61 / 20)
= 1 - P ( z < 47 / 20 )
= 1 - P ( z < 2.35 )
Using z table
= 1 - 0.9906
= 0.0094
Proportion = 0.0094
b ) P( x < 81 )
P ( x - / ) < ( 81 - 61 / 20)
P ( z < 20 / 20 )
P ( z < 1.00 )
= 0.8413
Proportion= 0.8413
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