Sections of rope are cut from a spool, after which each of the rope's two ends are cleanly trimmed and capped with a metal guard. The following information is known:
i) The lengths that result by cutting a section of rope from the spool are normally distributed with mean 1205 inches and variance 5 .
ii) The pieces trimmed from the two ends each have lengths that are normally distributed with mean 2 inches and variance 0.50 .
iii) Without variation, each of the two guards extends exactly one inch beyond the end of the rope to which the guard is attached.
iv) The three lengths mentioned in i) and ii) are mutually independent.
Calculate the probability that the finished product, measured guard tip to guard tip, is at least 1200 .
(A) 0.6915
(B) 0.8897
(C) 0.9101
(D) 0.9332
(E) 0.9999
380.2 Sections of rope are cut from a spool, after which each of the rope's two ends are cleanly trimmed and capped with a metal guard. The following information is known:
i)
The lengths that result by cutting a section of rope from the spool are normally distributed with mean 1205 inches and variance 5. ii) The pieces trimmed from the two ends each have lengths that are normally distributed with mean 2 inches and variance 0.50. ii) Without variation, each of the two guards extends exactly one inch beyond the end of the rope to which the guard is attached. iv) The three lengths mentioned in i) and ii) are mutually independent. Calculate the probability that the finished product, measured guard tip to guard tip, is at least1200.
(A) (B) (C) (D) (E)
0.6915 0.8897 0.9101 0.9332 0.9999
