Question

The manufacturer of a certain brand of aluminum foil claims that the amount of foil on each roll follows a Normal distribution with a mean of 250 square feet (ft^2) and a standard deviation of 2 ft^2 . To test this claim, a restaurant randomly selects 10 rolls of this aluminum foil and carefully measures the mean area to be ¯ = 249.6 ft2 .
Find the probability that the sample mean area is 249.6 ft^2 or less if the manufacturer’s claim is true.


0.4207


0.0228


0.5793


0.7364


0.2636

Answer 1

Answer: 0.4207

Step-by-step explanation:

Let $\overline{x}$ be the sample mean area.

Given: Population mean : $\mu=250$ sq. feet

Standard deviation: $\sigma=2$ sq. feet

Sample size : n= 10

The probability that the sample mean area is $249.6 \text{ ft}^2$ or less if the manufacturer’s claim is true.

$P(\overline{x}$

Required probability = 0.4207