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?

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

i would be 2,000 just get the square root of 50 which is 2500 and the divid 4/5 and last thing multiply the answer you get for that by the square root of 50

step-by-step explanation: