Question

The amount of icing on a Cuppie Cake large cupcake follows a Normal distribution, with a mean of 2 ounces and a standard deviation of 0.3 ounce. A random sample of 16 cupcakes is selected every day and measured. What is the probability the mean weight will exceed 2.1 ounces?

Answer 1

Answer: the probability the mean weight will exceed 2.1 ounces is 0.09

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