If the momentgenerating function of X is Mt exp 166t 200t2 f

If the moment-generating function of X is M(t) exp (166t +200t²), find

a.) The mean of X.

b.)the variance of X.

c.) P(170<X<200).

If the moment-generating function of X is M(t) exp (166t +200t²), find

exp (166t +200t²)= exp (166t +400t²/2),

a.) The mean of X. = 166

b.)the variance of X. = 400

c.) P(170<X<200).

Sd= sqrt( 400) =20

Z value for 170, z=( 170-166)/20 =0.2

Z value for 200, z=( 200-166)/20 =1.7

P(170<X<200) = P( 0.2<z<1.7) = p( z <1.7)