The histogram shows the distribution of stops for red traffic lights a commuter

Question

The histogram shows the distribution of stops for red traffic lights a commuter must pass through on her way to work. Use the histogram to find the mean, variance, standard deviation, and expected value of the probability distribution P(x) 0.4 0.30 0.20 0.10 0.04 0.0 0.35 25 140.13 0.09 0 1 2 3 45 The mean is (Round to two decimal places as needed.) The variance is Round to four decimal places as needed.) The standard deviation is Round to four decimal places as needed.) The expected value is Round to two decimal places as needed.)

Explanation / Answer

The mean = Sum(x * P(x) = 0*0.04 + 1*0.25 + 2*0.35 + 3*0.14 + 4*0.13 + 5*0.09 = 2.34

The Variance = Sum [x2 * P(x)] - Mean2.

Mean2 = 2.34 * 2.34 = 5.4756

Sum [x2 * P(x)] = 0 * 0.04 + 1 *0.25 + 4 * 0.35 + 9 * 0.14 + 16 * 0.13 + 25 * 0.05 = 7.24

Therefore Variance = 7.24 - 5.4756 = 1.7644

Standard Deviation = Sqrt(Variance) = Sqrt(1.7644) = 1.3283

Expected value = Mean = 2.34.

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