Question

snack food companies always have a target weight when filling a box of snack crackers. it is not possible, however, to always fill boxes to the exact target weight. for a particular box of crackers, the target weight is 14 ounces. the filling machine drops between 13.5 and 15 ounces of crackers into each box. let these weights be uniformly distributed. what is the probability that the weight in a box will be less than 14 ounces? what is the probability that the weight in a box will be between 14.5 and 15.5 ounces?

Answer 1

The probability that the weight in a box will be less than 14 ounces is 1, and the probability that the weight in a box will be between 14.5 and 15.5 ounces is 1.

Step-by-step explanation:

To find the probability that the weight in a box will be less than 14 ounces, we need to find the area under the probability density function (pdf) curve below 14 ounces. Since the weights are uniformly distributed between 13.5 and 15 ounces, the pdf is a rectangle with base 1.5 and height 1/1.5 = 2/3. The area of the rectangle represents the probability of the weight being less than 14 ounces. Therefore, the probability is (base * height) = 1.5 * (2/3) = 1.

To find the probability that the weight in a box will be between 14.5 and 15.5 ounces, we need to find the area under the pdf curve between 14.5 and 15.5 ounces. Since the pdf is a rectangle with base 1.5 and height 2/3, the area of the rectangle represents the probability of the weight being between 14.5 and 15.5 ounces. Therefore, the probability is (base * height) = 1.5 * (2/3) = 1.