Question

I work as a data analyst in Aeon Learning Pvt. Ltd. After analyzing data, I make
reports, where I have the efficiency of entering 77 words per minute with 6 errors per
hour. What is the probability that I will commit 2 errors in a 455-word financial report?
What happens when the no. of words increases/decreases (in case of 1000 words,
255 words)?
How is the ? affected?
How does it influence the PMF?
Give a pictorial representation of the same to validate your answer.

Answer 1

The time taken to write 455 words is

Expected number of errors in 5.909 minutes is

= 5.909/10 = 0.591

So the rate parameter

The pmf of a Poisson's distribution is

The probability that 2 errors will be committed in a 455-word report is

If the number of words increases, the time taken to write them will increase. If the time increases, the expected number of errors in that time period will increase. Hence, will increase.

If the number of words is 1000, then

Hence, has increased.

If the number of words decreases, the time taken to write them will decrease. If the time decreases, the expected number of errors in that time period will also decrease. Hence, will decrease.

If the number of words is 255, then

Hence, has decreased.

In the case when we want to know the probability of 2 errors, the more closer the is to 2, higher will be the probability. So, if the number of words increases to 1000, will increase to 1.299 which is closer to 2 than the case when the number of words decreases to 255 in which case decreases to 0.331 and gets farther from 2.

Hence, the probability of making 2 errors will increase if the number of words is increased, and the probability of making 2 errors will decrease if the number of words is decreased.

c) The graph when

The graph when the number of words increases to 1000 and is

The graph when the number of words decreases to 255 and is

As we can see, for higher number of words, the probability of making 2 errors (X=2) is the highest.

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