Question

Bottles of wine are stacked in racks of 12. The weights of these bottles are normally distributed with mean 1.3 kg and standard deviation 0.06 kg. The weights of the empty racks are normally distributed with mean 2 kg and standard deviation 0.3 kg. (i) Find the probability that the total weight of a full rack of 12 bottles of wine is between 17 kg and 18 kg.

Answer 1

you are given a normal distribution for the bottles themselves, and another normal distribution for the empty racks

you can add the two normal distributions together to get another normal distributions

the new mean is the sum of the two means
the new *variance* is the sum of the two variances (make sure to add variances, not standard deviations)

so once you have the new normal distributions, simply calculate the appropriate z-scores and probability values for 17 and 18kg and subtract accordingly

Answer 2

Thank you!!