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11Alexandr11 [23.1K]
3 years ago
13

The manufacturer of a certain brand of aluminum foil claims that the amount of foil on each roll follows a Normal distribution w

ith a mean of 250 ft2 and a standard deviation of 2 ft2. 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 ft2 or less if the manufacturer’s claim is true
Mathematics
1 answer:
lilavasa [31]3 years ago
7 0

Answer:

Given that the manufacturers claim is true, the probability that the sample mean area is 249.6 ft.² or less is 0.42074

Step-by-step explanation:

The manufacturer claims that mean amount of foil on each roll, μ = 250 ft²

The standard deviation of the measured amount of foil per roll, σ = 2 ft.²

The number of rolls tested by the restaurant, n = 10 rolls

The mean measured by the restaurant, \overline x = 249.6

Taking the sample means as individual score, we have;

The z-score, of the sample mean is given as follows;

z=\dfrac{\overline x -\mu }{\sigma }

At \overline x = 249.6, we have;

z = (249.6 - 250)/2 = -0.2

Therefore, the probability for a mean less than or equal to 249.6, we have;

The probability, P = P(z < -0.2) = 0.42074

The probability that the sample mean area is 249.6 ft.² or less given that the manufacturers claim is true, P = 0.42074.

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Since the question is asking how many pencils the teacher will have to give out, we can automatically ignore the 46 erasers from the problem because it is not relevant. The information was most likely put there to confuse you.

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