<p>The output of a chemical process is continually monitored to ensure that the

Question

<p>The output of a chemical process is continually monitored to ensure that the concentration remains within acceptable limits. Whenever the concentration drifts outside the limits, the process is shut down and re calibrated. Let X be the number of times in a given week that the process is re calibrated . The following table presents values of the cumulative function F(x) of x.<br /><br /><br /> x<br />&#160; &#160; &#160; &#160; &#160;0 &#160; &#160; &#160; 1 &#160; &#160; &#160;2 &#160; &#160; 3 &#160; &#160; &#160;4<br />F(x) 0.17, 0.53 0.84 0.97 1.00<br /><br />a. Compute mean of X,&#160;&#956;x.</p>
<p>b. what is the probability that the process is re calibrated fewer than two times during a week?</p>
<p>c. what is the probability that the process id re calibrated more than two times during a week?</p>
<p>d.what is the most probable number of recalibrated to occur during a week?</p>

Explanation / Answer

a)

P(X < 2) = F(1) = 0.53

b)

P(X > 2) = 1 - F(2) = 1 - 0.84 = 0.16

c)

P(X = 0) = 0.17

P(X = 1) = 0.53 - 0.17 = 0.36

P(X = 2) = 0.84 - 0.53 = 0.31

P(X = 3) = 0.97 - 0.84 = 0.13

P(X = 4) = 1 - 0.97 = 0.03

P(X=1) is bigger than other numbers, therefore the most probable number is X = 1.

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