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Answer:
10000*0.6065=6065
A. about 6,065
Step-by-step explanation:
Definitions and concepts
The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:
And the parameter represent the average ocurrence rate per unit of time.
For this distribution the expected value is the same parameter
,
,
Solution to the problem
We want "how many would have no blemishes" so first we need to find the probability that X=0, since X represent on this case the number of blemishes on each door. And if we use the mass function we got this:
And now since we have a total of 10000 doors painted we can find how many we would expect with no blemishes:
10000*0.6065=6065
A. about 6,065