A light fixture can be suspended from a ceiling at various heights using threade
ID: 3049660 • Letter: A
Question
A light fixture can be suspended from a ceiling at various heights using threaded suspension rods. The rods come in two lengths: the shorter rods have a nominal length of 6 inches and the longer rods have a nominal length of 18 inches. Suppose rods that have a nominal length of 6 inches actually come in lengths that are normally distributed with mean = 5.985 in and standard deviation = 0.12 in. Rods with a nominal length of 18 inches come in lengths that are normally distributed with = 17.985 in and standard deviation = 0.20 in.
(a) What is the probability that a randomly selected rod with a nominal length of 6 inches will be between 5.95 inches and 6.05 inches long?
(b) An electrical contractor purchases a dozen of the shorter rods for a lighting installation. Determine the probability that the mean length of the rods will be between 5.95 inches and 6.05 inches.
(c) A light can be suspended 18 inches using either a single long rod or three short rods threaded together. Which configuration is less likely to exceed a length of 18 inches, a single long rod or three connected short rods?
Explanation / Answer
a)
probability that a randomly selected rod with a nominal length of 6 inches will be between 5.95 inches and 6.05 inches long:
b)
probability that the mean length of the rods will be between 5.95 inches and 6.05 inches:
c)
for 6 inch 3 rods ; expected length =17.955
and std deviation =0.12*(3)1/2 =0.2078
hence probability to exceed a length of 18 inches
for 18 ich nominal rod:
probability to exceed a length of 18 inches:
threfore from above three connected short rods is less likely to exceed a length of 18 inches
for normal distribution z score =(X-)/ here mean= = 5.985 std deviation == 0.12Related Questions
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