Worked solution
Add a fixed box mass and retain both at-least-one methods
Pineapple masses in a large warehouse are normally distributed with mean 1.52 kg and standard deviation 0.070 kg. Six randomly chosen pineapples are packed in a box of mass 2.15 kg. Find the probability that the filled box has mass below 11.2 kg.
For 3 randomly chosen filled boxes, find the probability that at least 1 has mass below 11.2 kg.
[2005/II/23]
CJC · Discussion · Question 9
Answer
One filled box:0.342; at least one of three:0.715 (3 s.f.).
Model six independent pineapple masses
Let be a pineapple mass in kg. Under the source independent-sampling model, .
Shift the threshold by the fixed box mass
to 3 significant figures. The fixed packaging adds no variance.
Method 1: complement over three independent boxes
to 3 significant figures. Distinct boxes are treated as independent with the same probability.
Method 2: binomial count
Let X count the filled boxes below 11.2 kg. Then and to 3 significant figures. Both methods retain the source intermediate probability, rather than prematurely using 0.342.
Common mistakes
Use the unrounded one-box probability when computing the three-box probability.
Solution notes
Both asks, full source sum distribution/threshold shift, both source alternative methods, all intermediate and rounded values retained. Independent fruit/box sampling assumptions explicit; no marks printed.