SOLUTION: Please help me understand this can you please show me how you get your answers so i can understand it. A vending machine automatically pours soft drinks into cups. The amount

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Question 151425: Please help me understand this can you please show me how you get your answers so i can understand it.
A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6oz and standard deviation of 0.4oz. Examine figure 7.- and answer the following questions.
a) estimate the probability that the machine will overflow an 8oz cup.
b) Estimate the probabiltiy that the machine will not overflow an 8oz cup.
c) the machine has just been loaded with 850 cups. HOw many of these do you expect will overflow when served?
Please can you help me understand this
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6oz and standard deviation of 0.4oz. Examine figure 7.- and answer the following questions.
a) estimate the probability that the machine will overflow an 8oz cup.
Procedure:
Determine the z-score for 8
z(8) = (8-7.6)/0.4 = 0.4/0.4 = 1
P(x>8) = P(z>1) = 0.1587..
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b) Estimate the probabiltiy that the machine will not overflow an 8oz cup.
P(z<1) = 1 - 0.1587 = 0.8413..
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c) the machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?
0.1587*850 = 134.857..; Rounded down you get 134 cups
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Cheers,
Stan H.