Question 1182589
{{{P(X > 680) = P(Z = (X-mu)/sigma > (680-mu)/sigma) = 0.9788}}} ===> {{{(680-mu)/sigma = -2.030}}}, or {{{680 - mu = -2.030*sigma}}}.


Similarly,

{{{P(X > 700) = P(Z = (X-mu)/sigma > (700-mu)/sigma) = 0.0051}}} ===> {{{(700-mu)/sigma = 2.569}}}, or {{{700 - mu = 2.569*sigma}}}.


Now solve for {{{mu}}} and {{{sigma}}} from the two equations above. The values would be 


{{{sigma = 4.35}}} to 2 d.p., and {{{mu = 688.83}}} to 2 d.p.


===> {{{P(X > 648) = P(Z >  (648-688.83)/4.35 = -9.39) =  1}}}.


***We assume that lifetimes are normally distributed, and the probabilities were taken from https://stattrek.com/online-calculator/normal.aspx.