Drink Machine
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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 7.6 oz and standard deviation of 0.4 oz
(a) Estimate the probability that the machine will overflow an 8-oz cup.
(b) Estimate the probability that the machine will NOT overflow an 8-oz cup.
(c) The machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?
Given:
normal distribution sample
u = mean = 7.6 oz
s = standard deviation = 0.4 oz
Solution:
(a) P = ? for x > 8 oz
Solving for z yields
z = (x - u) / s = (8 - 7.6) / 0.4 = 1
From the z-tables P(1) = 0.8413 (answer to b) for x<= 8 oz, therefore x > 8 oz is
P(x>8) = 1 - 0.8413 = 0.1587 (15.87%)
(b) P = ? for x <= 8 oz
As derived from the z-tables (as shown above)
P = 0.8413 (or 84.13%)
(c) For N = 850 cups determine n with x > 8 oz.
n = N * P(x>8) = 850 (0.1587) = 134.9
= 135 cups
Here's a helpful site for TI-83/85 users http://mathbits.com/MathBits/TISection/Statistics2/normaldistribution.htm
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