Question

The useful life of one type of projector lamps has a normal distribution with a mean of 2250 hours and a standard deviation of 175 hours. Use X to denote the life of a projector lamp selected at random.

26. The probability that the useful life of a projector lamp selected at random is between 2100 and 2200 hours is closest to (2)

(A) 0.1141 (B) 0.3051 (C) 0.4192 (D) 0.1910 (E) none of the above

27. The probability that the useful life of a projector lamp selected at random is between 2200 and 2350 hours is closest to (2)

(A) 0.3298 (B) 0.2157 (C) 0.5714 (D) 0.1016 (E) none of the above

28. The lamp manufacturer is planning to offer a warranty on the useful lamp life. If the useful life is less than the warrantied useful life, represented by Xw , the manufacturer will offer a free replacement. If the manufacturer wants about 5% of the lamps to be replaced free, the warrantied life Xw should be closest to (5)

(A) 2540 (B) 2250 (C) 2000 (D) 1960 (E) 1900

Answer 1

26)

probability =

P(2100<X<2200)

=

P(-0.86<Z<-0.29)=

0.3859-0.1949=

0.1910

27)

probability =

P(2200<X<2350)

=

P(-0.29<Z<0.57)=

0.7157-0.3859=

0.3298

28)

for 5th percentile critical value of z=		-1.645
therefore corresponding value=mean+z*std deviation=			1962.13~ 1960