SOLUTION: The weight of potato chip packets is normally distributed with a mean of 510g and a standard deviation of 20g. Find the probability that a packet of chips will be below the labell

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Question 777895: The weight of potato chip packets is normally distributed with a mean of 510g and a standard deviation of 20g.
Find the probability that a packet of chips will be below the labelled weight of 500g.
A packet can only contain 550g otherwise it will overflow. Find the probability of a packet overflowing.
The lightest 5% of packets are rejected at quality control. At what weight does this occur?
What is the minimum weight of a packet that is in the heaviest 5%?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The weight of potato chip packets is normally distributed with a mean of 510g and a standard deviation of 20g.
Find the probability that a packet of chips will be below the labelled weight of 500g.
z(500) = (500-510)/20 = -1/2
P(x < 500g) = P(z < -1/2) = normalcdf(-100,-1/2) = 0.3085
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A packet can only contain 550g otherwise it will overflow. Find the probability of a packet overflowing.
z(550) = (550-510)/20 = 2
P(x > 550) = P(z > 2) = nomalcdf(2,100) = 0.0228
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The lightest 5% of packets are rejected at quality control. At what weight does this occur?
invnorm(0.02) = -2.0537
weight = -2.0537*20+510 = 468.93g
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What is the minimum weight of a packet that is in the heaviest 5%?
invNorm(0.95) = 1.645
weight = 1.645*20 + 510 = 542.90g
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Cheers,
Stan H.
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