The heights of 16-month-old oak seedlings are normally distributed with a mean of 31.5 cm and a standard deviation of 10 cm. What is the range of heights between which 75% of the seedlings will grow?

Question

tkhunny · Answer

Bad Question:  "will grow" is wrong.  It's not a matter of opinion.  It's wrong.  It should be "are expected to grow".

Bad Question:  There is not a unique answer.  "the range" is incorrect.  Does it want it symmetrical about the mean?

$(0,38.245)$ gives 75%
$(11.546,38.988)$ gives 75%
$(21.551,44.846)$ gives 75%
$(19.997,43.003)$ gives 75% <== The symmetric one.

anonymous · Answer

It's right out of the textbook. The back of the book has the symmetric answer. How did you come up with that?

tkhunny · Answer

The question needs to be severely rewritten.

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How many standard deviations from the mean will cut off 37.5% of the area?