A box contains 18 small items, of various lengths. The distribution of lengths in cm of the set of objects is (3,3,3,3,4

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A Box Contains 18 Small Items Of Various Lengths The Distribution Of Lengths In Cm Of The Set Of Objects Is 3 3 3 3 4 1 (132.44 KiB) Viewed 72 times

I only need the answer for question f). Thanks in advance.
A box contains 18 small items, of various lengths. The distribution of lengths in cm of the set of objects is (3,3,3,3,4,6,6,6,8,8,8,8,9,9,9, 11, 11, 11} (1) (a) (2 pts.) What is the probability that an object chosen at random from the box will have length 8 cm, assuming there is an equal probability of selecting any one object? (b) (2 pts.) What is the average length (L) (also called the expectation value of length) of an object in the box? (c) (2 pts.) What is the probability that an object chosen at random from the box will have length (L), assuming there is an equal probability of selecting any one object? (d) (2 pts.) What is the average of the square of the length (L´) of an object in the box? (e) (2 pts.) Use your previous results to compute the standard deviation o for the length of an item drawn from the box. (f) (4 pts.) What is the probability that an object chosen at random from the box will have length in the range (L) +o, assuming there is an equal probability of selecting any one object? Based on what you know about standard deviations, does this seem reasonable? Hint - think about the number of items in this distribution, and why that might matter