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Assignment05_OROUR - 5.31 a)% =30,=8 P(x)<0.4,z=1.28...

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5.31 a) Find a value of x such that 10% of x values are less than x 0 . µ  = 30,  σ  = 8 P(x) < 0.4, z = -1.28 -1.28 = (x - 30)/8 -1.28(8)+30 = x 19.76 = x b) find a value of x 0  such that 80% of x values are less than x 0 . P(x) < .3, z = 0.84 0.84 = (x - 30)/8 0.84(8) + 30 = x 36.72 = x c) find a value of x 0  such that 1% of x values are greater than x 0 . P(x) > .49, z = 2.32 2.32 = (x – 30)/8 2.32(8) + 30 = x 48.64 = x 5.38 a) Find the probability that weight will fall between 1,000 and 1,400 grams. µ  = 1,050,  σ  = 375 z = (x -  µ )/  σ z 1400  = (1400 – 1050) / 375 = 0.933 P(1400) = .3212
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z 1000  = (1000 – 1050) / 375 = -0.133 P(1000) = .0517 P(1400) + P(1000) = .3212 + .0517 = .3755 b) Find the probability that the weight will fall between 800 and 1,000 grams. Z 1000  = -0.133, P(1000) = .0517 Z 800  = (800 – 1050)/375 = -0.667 P(800) = .2486 P(800) – P(1000) = .2486 – 0.0517 = .1969 c) Find the probability that the weight will be less than 1,750 grams.
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