A wire is uniformly distrubuted on the interval (2.0, 3.5) but is considered fun

Question

A wire is uniformly distrubuted on the interval (2.0, 3.5) but is considered functional only between (2.2,3.4). a) What is the probability that wire cannot be used? b) Compute mean and variance. c) if someone has wire with same mean and variance as in b, but the distribution of is normal. Should she switch the wire? A wire is uniformly distrubuted on the interval (2.0, 3.5) but is considered functional only between (2.2,3.4). a) What is the probability that wire cannot be used? b) Compute mean and variance. c) if someone has wire with same mean and variance as in b, but the distribution of is normal. Should she switch the wire?

Explanation / Answer

a)  probability that wire cannot be used =1-P(used)=1-(3.4-2.2)/(3.5-2)=0.2

b) mean is (a+b)/2 or (2+3.5)/2=2.75

variance is ((b-a)^2) /12 =((3.5-2)^2) /12 =0.1875

c) We should switch the wire

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