3.6-16 If the moment-generating function of X is M(t) = e^(500t+5000t^2), find P[27,060 (less than or equal to) (X-500)^2 (less than equal to) 50,240]

3.6-17 If X is N(7,4), find P[15.364 (less than or equal to) (X-7)^2 (less than or equal to) 20.096].

3.6-18 The strength X of a certain material is such that its distribution is found by X = e^Y, where Y is N(10,1). Find the distribution function and p.d.f. of X and computer P(10,000 < X < 20,000).

Note: The random variableX is said to have a lognormal distribution.

This solution provides calculations with normal distributions.