An apiculturalist investigating the effect of nutrition on bee morphology, weigh

Question

An apiculturalist investigating the effect of nutrition on bee morphology, weighed 16 worker bee pupae from a commercial hive. She found that the average weight was 530 mg with a standard deviation of 36 mg. (a) Ten per cent of the pupae will have weights below that required for developing into a worker designated for gathering food, what is the pupae weight below which the bees will be too small to be considered for gathering food for the hive? (b) The middle 80 per cent of the pupae can develop into workers that can be chosen for any of the hive task, between what two weights will the middle 80% fall? (c) Only those bee pupae that weigh in the top one (1) percent of the population will develop into bees that will become defenders of the hive. What is the minimal pupae weight of bees that might become a defender of the hive?

Explanation / Answer

Given = 530mg, =36mg

Z = (X- )/ = (X – 530 )/36

Given percent of pupae weighing less than X = 10%

P(Weight<X) = 0.1

P(Z < (X – 530)/36) = 0.1

From normal distribution table z value for 0.1 is -1.28155

Z = (X-530)/36 = -1.28155

X < 483.864

We have already got the value of z for bottom and top 10% as -1.28155 and +1.28155

Therefore the limit for hive task is

-1.28155 < Z < 1.28155

-1.28155 < (X – 530)/36 < 1.28155

483.864 < X < 576.1358

c) To become defender we need the top 10%

Z value for it is 1.28155

Z > 1.28155

(X-530)/36 > 1.28155

X > 576.1358

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