The auto parts department of an automotive dealership sends out a mean of 4.7 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 3? Round your answer to four decimal places.

0.1574

Step-by-step explanation:

We are given that

Mean=4.7

We have to find the probability that for any day the number of special order sent out will  be exactly 3.

We know that by Poisson distribution

Where

Using the formula

Hence, the probability that for any day,the number of special orders sent out will be exactly 3=0.1574

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

could you provide figure.