Question

Could you please breakdown the steps involved, please.

In talking to their auditors, a production manager becomes concerned about the weight of their marinated chilli's products. In particular, the manager notes two constraints: weights must be acceptable in terms of a) containing an amount equal or more than the given contents displayed on the package label; and b) contain less than a given constraint based on wastage. The two constraints for the marinated chilli's are listed as 500g and 505g respectively. Based on the auditors' requests, the manager monitors a sample of bottles' weights. There doesn't appear to be any pattern in the weights and all fall between the two weights. What is the probability that the weight of a randomly selected bottle would be:

i) 502g or less? ii) 504g or more? iii) Between 502g and 504g? iv) Between 502g and 506g?

Answer 1

Let X be a random variable which denotes the weight(in gram) of a randomly selected bottlle.

From the first constraint , we get that X should be greater than or equal to 500

And from the second constraint, we get that X should be less than 505

Thus combining both the constraints, we get that

500 <= X < 505

Now as it given that there doesn't appear any pattern in the weights, we can say that X follows Uniform distribution.

(i) P( X <= 502) = (502 - 500)/(505 - 500) = 0.4

(ii) P( X >= 504) = (505 - 504)/(505 - 500) = 0.2

(iii) P( 502 <= X <= 504) = (504 - 502)/(505 - 500) = 0.4

(iv) P( 502 <= X <= 506)

= P( 502 <= X <= 505) + P(505 < X <= 506)

= (505 - 502)/(505 - 500) + 0

= 0.6