3. The amount of hot chocolate dispensed by a hot chocolate machine is normally distributed with a mean of 16.0 oz and a standard deviation of 2 oz. If the cups hold 18.0 oz, what is the probability that a selected cup will be overfilled

Answer: the probability that a selected cup will be overfilled is 0.16

Step-by-step explanation:

Since amount of hot chocolate dispensed by a hot chocolate machine is normally distributed,

we would apply the formula for normal distribution which is expressed as

z = (x - µ) / σ

Where

x = amount of hot chocolate dispensed by a hot chocolate machine.

µ = mean

σ = standard deviation

From the information given,

µ = 16.0 oz

σ = 2 oz

We want to find the probability that a selected cup will be overfilled. Since the cup can hold 18.0 oz, the expression would be

P (x > 18) = 1 - P (x ≤ 18)

For x = 18,

z = (18 - 16) / 2 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.84

P (x > 18) = 1 - 0.84 = 0.16