Homework 8 Solutions - Engineering Statistics | STAT 305, Assignments of Statics

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Stat 305 (Ghosh): HW8 Solutions ie P323 7 The probability of one part failing to meet inspection is equal to the long-run fraction of parts } —~ failing to meet inspection, if the part measurements are considered to be identical random variables. You need to make small enough so that P(X > 3.150) < .03. This is equivalent to P(X < 3.150) > .97, which is equivalent to P(Z < 2489=#) > 197, where Z is a standard normal random variable. Looking up .97 in the body of Table BS 3.150 — p 8 002 > 1.88, or ¢ < 3.14624. Pe 39 2. (a) The probability of an individual depth being within specifications is the same as the ——— long-run fraction of depths within specifications, if successive shelf depths can be considered identical random variables. P(.0275 < X <.0278) = P(X <.0278) ~ P(X < .0275) P(Z<2)-P(Z<-1) .9773 — .1587 = 8186. (Z is a standard normal random variable.) (b) Assuming that p = .02765, we want P(.0275 < X < .0278) = .98. By symmetry, this is equivalent to P(X < .0278) = .99, which is equivalent to Pp (2 < -0278 ~ an = 99 oc Looking up .99 in the body of Table 8,3, this means that 00015 or that o ~ .00006438.