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.) (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 808 cups. How many of these do you expect will overflow when served? cups

Answer 1

a)

Here, μ = 7.6, σ = 0.4 and x = 8. We need to compute P(X >= 8). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (8 - 7.6)/0.4 = 1

Therefore,
P(X >= 8) = P(z <= (8 - 7.6)/0.4)
= P(z >= 1)
= 1 - 0.8413 = 0.1587

b)

Here, μ = 7.6, σ = 0.4 and x = 8. We need to compute P(X <= 8). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (8 - 7.6)/0.4 = 1

Therefore,
P(X <= 8) = P(z <= (8 - 7.6)/0.4)
= P(z <= 1)
= 0.8413

c)

0.1587 * 808 = 128 cups