μ = 12
σ = 0.4
a) P (X > 12.12)
We are given that the distribution of weights of ice cream cartons is a normal distribution. Formula:
[tex]Z\text{ score = }\frac{x\text{ - }\mu\text{ }}{\sigma}[/tex]P (X > 12.12) = P (Z > 0.3) = 1 - P(Z ≤ 0.3) = 1 - 0.618 = 0.382
b) P(weight of 36 randomly selected cartons is greater than 12.12 ounces)
Now, as we are working with a sample, the formula will be:
[tex]Z\text{ score = }\frac{x\text{ - }\mu\text{ }}{\frac{\sigma}{\sqrt[]{n}}}[/tex]P (X > 12.12) = P (Z > 1.8) = 1 - P(Z ≤ 1.8) = 1 - 0.964 = 0.036
