Question

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.

Answer 1

Answer:

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 $X \sim Poisson(\lambda=24.7)$

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

$f(x)=\frac{e^{-\lambda} \lambda^x}{x!} , x=0,1,2,3,4,...$

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 $X \sim Poisson(\lambda=24.7)$

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

$f(x)=\frac{e^{-\lambda} \lambda^x}{x!} , x=0,1,2,3,4,...$

And f(x)=0 for other case.

For this distribution the expected value is the same parameter $\lambda$

$E(X)=\mu =\lambda$

And for this case we want to calculate this probability:

$P(X \geq 10)$

The best answer for this case would be:

C. Poisson distribution

Answer 2

Solution :

Given that ,

mean = $\mu$ = 24.7

P(X $\geq$10)

C) This is the poisson distribution .