Question

1.The time it takes an assembly line worker to complete a task is exponentially distributed with a mean of 8 minutes.
a. Calculate the probability that it will take a worker less than 4 minutes to complete the task.
b. Calculate the probability that it will take a worker more than 4 minutes to complete the task.
c. Calculate the probability that it will take a worker exactly 4 minutes to complete the task. Explain your answer.

Answer 1

Answer:

a. 3/8

b . 1/2

c. 1/8

Step-by-step explanation:

probability = no of chances/ total

a. less than four minutes mean it's 1 min , 2 min, 3min. so 3/8

b. more than 4 minutes means it's 5 min, 6min, 7 min, 8 min. so it's 4/8 thn it's processed to 1/2

c. exactly 4 min means it have 1 probability so it's 1/8.

I hope it helped u buddy...

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Answer 2

Given: The time it takes an assembly line worker to complete a task is exponentially distributed with a mean of 8 minutes.

To find: a. The probability that it will take a worker less than 4 minutes to complete the task.

b. The probability that it will take a worker more than 4 minutes to complete the task.

c. The probability that it will take a worker exactly 4 minutes to complete the task.

Solution: Probability is given by the formula = Number of favourable outcomes/Total number of outcomes.

Total number of outcomes = 8.

a. Since it says less than 4 minutes, so the favourable outcomes are 1, 2 and 3.

Therefore, the probability that it will take a worker less than 4 minutes to complete the task = 3/8.

b. Since it says more than 4 minutes, so the favourable outcomes are 5, 6, 7 and 8.

Therefore, the probability that it will take a worker more than 4 minutes to complete the task = 4/8 =1/2.

c. Since it says exactly 4 minutes, so there is only one favourable outcome which is 4.

Therefore, the probability that it will take a worker exactly 4 minutes to complete the task = 1/8.

Answer: a. 3/8

              b. 1/2

              c. 1/8