A statistics professor finds that when she schedules an office hour for student help, an average of 3.3 students arrive. Find the probability that in a randomly selected office hour, the number of student arrivals is 3.

0.2209 = 22.09% probability that in a randomly selected office hour, the number of student arrivals is 3.

Step-by-step explanation:

We have the mean during an interval, so the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given interval.

A statistics professor finds that when she schedules an office hour for student help, an average of 3.3 students arrive.

This means that

Find the probability that in a randomly selected office hour, the number of student arrivals is 3.

This is P(X = 3). So

0.2209 = 22.09% probability that in a randomly selected office hour, the number of student arrivals is 3.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18