The probability density function of the length of a hinge for fastening a door is f(x)=1.25 for 74.6 < x < 75.4 for millimeters. Determine the following:
a) P(X<75.4)=?
b)P(X<74.8 or X > 75.2)
c)If the specifications for this process are from 74.7 to 75.3 millimeters, what proportion of hinges meets specifications?
2007-11-20 15:58:28 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The probability is constant throughout the interval 74.6 to 75.4, and 0 outside that interval. Since the length of that interval is 8/10 mm, each 1/10 mm has a probability of 1/8, or 0.125.
2007-11-20 16:24:01
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answer #1
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answered by jim n 4
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(a) Since the entire probability for the length is < 75.4, P(X < 75.4) = 1.
(b) X < 74.8 includes 2/10 mm of the possible range, or a probability of 2*0.125. Also, X > 75.2 includes 2/10 mm of the possible range, so P(X > 75.2) = 2*0.125 = 0.25
So P(X<74.8 or X > 75.2) = P(X<74.8) + P(X>75.2) = 0.25 + 0.25 = 0.5
(c) The specs are from 74.7 to 75.3, which is a distance of 6/10 mm, so
P(74.7
Draw a picture. What you will see is an uniform distribution from 74.6 to 75.4 mL. f(x) has to be 1.25 since SUM(f(x)) in all x-space=1. The rest should be pretty straightforward.
2007-11-20 16:03:04 · answer #2 · answered by cattbarf 7 · 0⤊ 0⤋