Question

A manufacturer produces sweets of length L mm where L has a continuous uniform distribution with a range [6, 24]. What is the probability that a randomly selected sweet is between 10 mm and 18 mm in length?

Answer 1

The probability that a randomly selected sweet is between 10 mm and 18 mm in length is 4/9.

Step-by-step explanation:

To find the probability that a randomly selected sweet is between 10 mm and 18 mm in length, we can use the concept of a continuous uniform distribution. In this case, the length of the sweets has a continuous uniform distribution with a range of [6, 24].

First, we need to find the probability of a sweet being less than 10 mm in length and the probability of a sweet being less than 18 mm in length.

P(L < 10) = (10-6)/(24-6) = 4/18 = 2/9

P(L < 18) = (18-6)/(24-6) = 12/18 = 2/3

To find the probability of a sweet being between 10 mm and 18 mm in length, we subtract the probability of it being less than 10 mm from the probability of it being less than 18 mm.

P(10 < L < 18) = P(L < 18) - P(L < 10) = 2/3 - 2/9 = 4/9

Therefore, the probability that a randomly selected sweet is between 10 mm and 18 mm in length is 4/9.

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