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The amount of time needed for a certain machine to process a job is a random variable with mean EXi = 10 minutes and Var(Xi)=2 minutes2. The times needed for different jobs are independent from each other. Find the probability that the machine processes less than or equal to 40jobs in 7hours.

Sagot :

fichoh

Answer:

0.98732

Step-by-step explanation:

Given that :

Mean = 10 minutes

Variance = 2 minutes

For less than equal 40 jobs

Mean (m) = 40 * 10 = 400 minutes

Variance = 2 * 40 = 80 minutes

Standard deviation (s) = √variance = √80

Converting hours to minutes

X = 60 * 7 = 420 minutes

P(X≤ 420) :

Z = (x - m) / s

P(X≤ 420) :

Z = (420 - 400) / √80

Z = 20 / √80 = 20 / 8.9442 = 2.236

P(Z ≤ 2.236) = 0.98732

The probability that the machine processes less than or equal should be 0.98732

Calculation of the probability:

Since

Mean = 10 minutes

Variance = 2 minutes

For less than equal 40 jobs

Mean (m) = 40 ( 10) = 400 minutes

Variance = 2 (40) = 80 minutes

Now

Standard deviation (s) = √variance = √80

Now here we Converting hours to minutes

So,

X = 60 (7) = 420 minutes

Now

P(X≤ 420) :

Z = (x - m) / s

Z = (420 - 400) / √80

Z = 20 / √80

= 20 / 8.9442

= 2.236

Now finally

P(Z ≤ 2.236)

= 0.98732

Hence, The probability that the machine processes less than or equal should be 0.98732

Learn more about probability here: https://brainly.com/question/3066522

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