## [answered] 12. Dentists now use porcelain for filling teeth instead of

12. Dentists now use porcelain for filling teeth instead of silver amalgam, which was used in the past. However, porcelain fillings do not last as long as silver amalgam. In fact, the mean life of a porcelain filling is 40 months, while that of an amalgam filling is 75 months. If it is known that the lives of both types of filling are normally distributed with the same variance of 5 months, what is the probability that an amalgam filling will last at least twice as long as a porcelain filling? (A) .5000 (B) .5636 (C) .5398 (D) .1587 (E) .8413 If X is the life of an amalgam filling and Y is the life of a porcelain filling, X ? 2Y ~ N(75 ? 80,5 + (22 - 5)) = N(?5,25). Therefore P(X 2 21/) = P(X ? 2y 2 0) = 1 ? @(M?E?) = 1 ? <1>(1) = .1587.
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can you explain what ? would be here? i don't understand also how the got 25 (i know why they got 5 but not how they got 2^2)
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