6. Fun with statistics (12 pts). To do this problem, while you may use a calcula

Question

6. Fun with statistics (12 pts). To do this problem, while you may use a calculator, spreadsheet or mathematical software to do simple algebraic operations like adding and dividing, don't use any built-in statistics functions 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 a) 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) What is the average length (also called the expectation value of length) of an object in the box? c) What is the probability that an object chosen at random from the box will have length

Explanation / Answer

Ans:

a)P(X=8)=4/18=0.222

b)Average length=126/18=7

c)Probability of choosing object of any length=frequency count/18

Say ,probability of choosing object of length 9=3/18=1/6=0.167

d)Average of L2=1022/18=56.78

e)Variance=E[L2]-(E[L])2

=56.78-72

=56.78-49

=7.78

standard deviation=sqrt(7.78)=2.789

Object length(L) L2 1 3 9 2 3 9 3 3 9 4 3 9 5 4 16 6 6 36 7 6 36 8 6 36 9 8 64 10 8 64 11 8 64 12 8 64 13 9 81 14 9 81 15 9 81 16 11 121 17 11 121 18 11 121 Total= 126 1022 Mean= 7 56.78

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