Answer: the probability the mean weight will exceed 2.1 ounces is 0.09
Step-by-step explanation:
Let x be the random variable representing the amount of icing on a Cuppie Cake large cupcake. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = standard deviation
n = number of samples
From the information given,
µ = 2
σ = 0.3
n = 16
x = 2.1
the probability that the mean weight will exceed 2.1 ounces is expressed as
P(x ≥ 2.1)
For x = 2.1
z = (2.1 - 2)/(0.3/√16) = 1.33
We would determine the probability for the area above z = 1.33 from the normal distribution table. It would be
p = 1 - 0.91 = 0.09
P(x ≥ 2.1) = 0.09
