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16.116.4 Assessment Answers
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16.1  Determine the missing probability
0.04
All probabilities must add up to 1.00 (or 100%)
16.2  Calculate expected value and standard deviation, then interpret in context
E(Red Lights) = 0*.02 + 1*.07 + 2*.15 + ... + 6*.01 = 2.93
Over the long run, the average number of red lights hit on each drive to school will be 2.93
sigma (Red Lights) = 1.01
Var(Red Lights) = (1.01)^2
Over the long run, the amount of variability (standard deviation) in number of red lights hit on a drive to school is 1.01
16.3  Determine new E(X) and sigma(X) when adding by a constant or multiplying by a constant
If wait time is 3 minutes at each red light, then multiply all red light values by 3...
Wait Time = 3*Red Lights
E(Wait Time) = E(3*Red Lights) = 3*E(Red Lights) = 3*2.93 =
sigma(Wait Time) = E(3*Red Lights) = 3*E(Red Lights) = 3*1.01 =
Var(Wait Time) = (3*1.01)^2
16.4  Variances Add
Difference In Wait Times = Your Time  Friend's Time
E(Difference In Wait Times) = E(Your Time)  E(Friend's Time)
Var(Difference In Wait Times) = Var(Your Time)
+
Var(Friend's Time) <<Variances Add...ALWAYS>>
sigma(Wait Time) = sqrt(Var(Difference In Wait Times))
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0.04
All probabilities must add up to 1.00 (or 100%)
16.2  Calculate expected value and standard deviation, then interpret in context
E(Red Lights) = 0*.02 + 1*.07 + 2*.15 + ... + 6*.01 = 2.93
Over the long run, the average number of red lights hit on each drive to school will be 2.93
sigma (Red Lights) = 1.01
Var(Red Lights) = (1.01)^2
Over the long run, the amount of variability (standard deviation) in number of red lights hit on a drive to school is 1.01
16.3  Determine new E(X) and sigma(X) when adding by a constant or multiplying by a constant
If wait time is 3 minutes at each red light, then multiply all red light values by 3...
Wait Time = 3*Red Lights
E(Wait Time) = E(3*Red Lights) = 3*E(Red Lights) = 3*2.93 =
sigma(Wait Time) = E(3*Red Lights) = 3*E(Red Lights) = 3*1.01 =
Var(Wait Time) = (3*1.01)^2
16.4  Variances Add
Difference In Wait Times = Your Time  Friend's Time
E(Difference In Wait Times) = E(Your Time)  E(Friend's Time)
Var(Difference In Wait Times) = Var(Your Time) + Var(Friend's Time) <<Variances Add...ALWAYS>>
sigma(Wait Time) = sqrt(Var(Difference In Wait Times))