1. Suppose that you’d like to know how reliable your friends are. So you go talk

Question

1.       Suppose that you’d like to know how reliable your friends are. So you go talk to two of your friends, the first one is not very interested in recycling. And tells you how many days that he/she recycles in a month. And you talk to another friend who is more interested in recycling and that friend gives you an estimate of the number of days that he/she recycles in a month. So you use these two values to create a uniform problem. So imagine you make up your own numbers for your two values. Draw a picture that helps you. And use the spreadsheet that I gave you early in the semester.

a.       Determine the mean for your problem.

b.       Determine the standard deviation.

c.       Based on your distribution what’s the likelihood that a random friend of yours is within one standard deviation of the mean?

d.       Discuss your results.

Explanation / Answer

let the first person choose a

and second persom choose b

where b>a

mean of a uniform distribution = .5(a+b)

variance = 1/12 (b-a)^2

sd = sqrt(1/12) (b-a)

one SD of the mean

P(.5(a+b) - sqrt(1/12 (b-a)^2) <x< .5(a+b) +sqrt(1/12 (b-a)^2) )

= 2(sqrt(1/6(b-a)^2)/(b-a) = 2/sqrt(12) = 1/sqrt(3) =.577

d)

for a uniform distribution the probabilty that a number will be in one SD will be ~.577 and is constant.

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