A vending machine automatically pours soft drinks into cups. The amount of soft

Question

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 ounces and standard deviation of 0.4 ounce. Examine the figure below and answer the following questions.

(a) Estimate the probability that the machine will overflow an 8-ounce cup. (Round your answer to two decimal places.)
1

    (b) Estimate the probability that the machine will not overflow an 8-ounce cup. (Round your answer to two decimal places.)
2

    (c)  The machine has just been loaded with 880 cups. How many of these do you expect will overflow when served?
3 cups

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 ounces and standard deviation of 0.4 ounce. Examine the figure below and answer the following questions. (a) Estimate the probability that the machine will overflow an 8-ounce cup. (Round your answer to two decimal places.) (b) Estimate the probability that the machine will not overflow an 8-ounce cup. (Round your answer to two decimal places.) (c) The machine has just been loaded with 880 cups. How many of these do you expect will overflow when served?

Explanation / Answer

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

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