Question 959416: The mean weight of a box of cereal filled by a machine is 15.0 ounces, with a standard deviation of 0.4 ounce. If the weights of all the boxes filled by the machine are normally distributed, what percent of the boxes will weigh the following amounts? (Round your answers to two decimal places.)
(a) less than 14.5 ounces
? %
(b) between 14.7 and 15.3 ounces
? %
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The mean weight of a box of cereal filled by a machine is 15.0 ounces, with a standard deviation of 0.4 ounce. If the weights of all the boxes filled by the machine are normally distributed, what percent of the boxes will weigh the following amounts? (Round your answers to two decimal places.)
(a) less than 14.5 ounces
z(14.5) = (14.5-15)/0.4 = -1.25
P(x < 14.5) = P(z < -1.25) = 0.1057
10.57 %
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(b) between 14.7 and 15.3 ounces
z(15.3) = (15.3-15)/0.4 = 0.3/0.4 = 0.75
z(14.7) = (14.7-15)/0.4 = -0.3/0.4 = -0.75
P(14.7< x < 15.3) = P(-0.75< z <0.75) = 0.5468
54.68 %
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Cheers,
Stan H.
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