The maintenance department at Kruger Industrial Smoothing estimates that it take
ID: 3209356 • Letter: T
Question
The maintenance department at Kruger Industrial Smoothing estimates that it takes between one and four hours to performance preventive maintenance on a broken grinding machine. The probability distribution is shown in the table.
Calculate the mean and standard deviation of the probability distribution of maintenance times.
What is the probability that maintenance takes at least two hours?
Maintenance time (to nearest half hour) 1 -------1.5 --------2 --------2.5--------- 3 ----------3.5 --------4
Probability ----------------------------------------0.06--- 0.18-- --- 0.28----0.22---------0.14------ 0.08-----0.04
Explanation / Answer
mean, E(X) = 1 * 0.06 + 1.5 * 0.18 + 2 * 0.28 + 2.5 * 0.22 + 3 * 0.14 + 3.5 * 0.08 + 4 * 0.04
= 2.3
E(X2) = 12 * 0.06 + 1.52 * 0.18 + 22 * 0.28 + 2.52 * 0.22 + 32 * 0.14 + 3.52 * 0.08 + 42 * 0.04
= 5.84
Var(X) = E(X2) - (E(X))2
= 5.84 - 2.32
= 0.55
Stadard deviation = sqrt(0.55) = 0.742
P(X > 2) = 1 - [P(X < 2)]
= 1 - [P(X = 1) + P(X = 1.5)]
= 1 - [0.06 + 0.18]
= 0.76
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