A professor receives, on average, 24.7 emails from students the day before the midterm exam. To compute the probability of receiving at least 10 emails on such day, he will use what type of probability distribution?A. binomial distribution
B. hypergeometric distribution
C. Poisson distribution
D. none of the above.

Let X the random variable that represent the number of emails from students the day before the midterm exam. For this case the best distribution for the random variable X is

The probability mass function for the random variable is given by:

The best answer for this case would be:

C. Poisson distribution

Step-by-step explanation:

Let X the random variable that represent the number of emails from students the day before the midterm exam. For this case the best distribution for the random variable X is

The probability mass function for the random variable is given by:

And f(x)=0 for other case.

For this distribution the expected value is the same parameter

And for this case we want to calculate this probability:

The best answer for this case would be:

C. Poisson distribution

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

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