IQ scores in a certain population are normally distributed w

IQ scores in a certain population are normally distributed with a mean of 95 and a standard deviation of 11. (Give your answers correct to four decimal places.)

(a) Find the probability that a randomly selected person will have an IQ score between 81 and 103.


(b) Find the probability that a randomly selected person will have an IQ score above 80.

Solution

(a) Find the probability that a randomly selected person will have an IQ score between 81 and 103.

P(81<X<103) = P((81-95)/11<(X-mean)/s <(103-95)/11)

=P(-1.27<Z<0.73) =0.6653 (from standard normal table)

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(b) Find the probability that a randomly selected person will have an IQ score above 80.

P(X>80) = P(Z>(80-95)/11)

=P(Z>-1.36) = 0.9131 (from standard normal table)