Mr. Smith works on a temporary basis. The mean length of each job he gets is three months. If the amount of time he spends between jobs is exponentially distributed with mean 2, then at what rate does Mr. Smith get new jobs?

Mr Smith gets a new job, every 5 months on the average.

Step-by-step explanation:

Mr Smith spends an average of 3 months on every job he gets.

Then he spends an average of 2 months in between jobs.

Meaning, on the average, if he has a job, he does it for 3 months, then leaves, lends the next 2 months without a job, then gets another job at the end of the 2 months without a job and then he repeats the cycle of 3 months on the job, 2 months without the job.

So, on the average it takes Mr. Smith, (3+2) months to get a new job.

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean =

also, median= , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean =  

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.

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step-by-step explanation: