A company sells cookies in 250-gram packs. When a particular batch of 1,000 packs was weighed, the mean weight per pack was 255 grams and the standard deviation was 2.5 grams. Assuming the data is normally distributed, we can conclude that % of the packs weighed less than 250 grams.

Question

Mathematics

Maximilian Hooper

11 December, 03:18

A company sells cookies in 250-gram packs. When a particular batch of 1,000 packs was weighed, the mean weight per pack was 255 grams and the standard deviation was 2.5 grams. Assuming the data is normally distributed, we can conclude that % of the packs weighed less than 250 grams.

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Lucky · Answer 1

Let X be a random variable representing the weight of a pack of cookies.

P (X < 250) = P (z < (250 - 255) / 2.5) = P (z < - 5/2.5) = P (z < - 2) = 1 - P (z < 2) = 1 - 0.97725 = 0.02275 = 2.3%

Therefore, we conclude that about 2.3% of the packs weighed less than 250 grams.