2. The length of time a system is \"down\" (that is, broken) is described (appro

Question

2. The length of time a system is "down" (that is, broken) is described (approximately) by the probability distribution in the Table 7.6.2. Assume that these downtimes are exact. That is, there are three types of easily recognized problems that always take this long (5, 30, or 120 minutes) to fix.

Explain the process of all the questions

Probability Distribution of downtime

Problem

Downtime (minutes)

Probability

Minor

5

0.60

Substantial

30

0.30

Catastrophic

120

0.10

a. What kind of probability distribution does this table represent?

b. Find the mean downtime.

c. Find the standard deviation of the downtime.

d. What is the probability that the downtime will be greater than 10 minutes, according to this table?

e. What is the probability that the downtime is literally within one standard deviation of its mean? Is this about what you would expect for a normal distribution?

Probability Distribution of downtime

Problem

Downtime (minutes)

Probability

Minor

5

0.60

Substantial

30

0.30

Catastrophic

120

0.10

Explanation / Answer

f=   0.31  
fx =   16.8  
      
Mean = fx / f =   54.1935  
Mean square = f x^2 / f =   5085.4839  
      
Varriance = (Mean square) - (Mean)^2      
      
Varriance = f x^2 - Mean^2 =   2148.548  
Stadard Dev= Var =   46.352  

[ANSWERS]

a. Grouped data, discrete distributions

b. Mean = 54.1935  

c. S.D = 46.352

d.

P(X>10) = P(30)+P(120) = 0.15+0.1 = 0.25

Note: As - per chegg, experts - only - solve - 4- sub parts - in - a - question -per -thread. Please -ask -the -remaining -in -different- post

Values ( X ) Frequency(f) fx ( X^2) f x^2 5 0.06 0.3 25 1.5 30 0.15 4.5 900 135 120 0.1 12 14400 1440

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