Suppose that Z denotes a standard normal random variable Fin

Suppose that Z denotes a standard normal random variable. Find: (a) P(Z > 2.23) (b) (-1.22

Solution

(a) P(Z>2.23) =0.0129 (from standard normal table)

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(b)P(-1.22<Z<3.05) =0.8876 (from standard normal table)

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(c) P(-k<Z<k)= 0.95

--> 2*P(0<Z<k) =0.95

--> P(0<Z<k) = 0.95/2 =0.475

--> P(Z<k) - P(Z<0) =0.475

--> P(Z<k) - 0.5 =0.475

--> P(Z<k) =0.475+0.5 =0.975

So k =1.96 (from standard normal table)