Question

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?

Answer #1

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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