Suppose that blood chloride concentration mmolL has a normal

Suppose that blood chloride concentration (mmol/L) has a normal distribution with mean 105 and standard deviation 6. 2.1. (2pts) What is probability that chloride concentration is at most 106? 2.2. (2pts) What is probability that chloride concentration is greater than 113.2? 2.3. (2pts) What is probability that chloride concentration is between 100 and 110? 2.4. (2pts) Determine the 90th percentile value of chloride concentration (hint. Find x such that P(X

Solution

(1)P(X<106) = P((X-mean)/s <(106-105)/6)

=P(Z<0.17) =0.5675 (from standard normal table)

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(2)P(X>113.2) = P(Z>(113.2-105)/6)

=P(Z>1.37) =0.0853(from standard normal table)

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(3) P(100<X<110) = P((100-105)/6<Z<(110-105)/6)

=P(-0.83<Z<0.83) =0.5935 (from standard normal table)

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(4) P(X<x)=0.9

--> P(Z<(x-105)/6) =0.9

--> (x-105)/6 = 1.28 (from standard normal table)

So x= 105+1.28*6=112.68