Suppose a botanist grows many individually potted eggplants, all treated identic

Question

Suppose a botanist grows many individually potted eggplants, all treated identically and arranged in groups of four pots on the greenhouse bench. After 30 days of growth, she measures the total leaf area Y of each plant. Assume that the population distribution of Y is approximately normal with mean = 800cm^2 and SD = 90cm^2.
a) What percentage of the plants in the population will have leaf area between 750cm^2 and 850cm^2?
b) Suppose each group of four plants can be regarded as a random sample from the population. What percentage of the groups will have a group mean leaf area between 750cm^2 and 850cm^2?

Explanation / Answer

a) normalcdf(750,850,800,90) = 0.4215 b) normalcdf(750,850,800,90/sqrt(4)) = 0.7335

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