Some nations require their students to pass an exam before earning their primary school degrees or domas. A certain nation gives students an exam whose scores are normally distributed with a mean of 41 points and a
standard deviation of 9 points
Suppose we select 2 of these testers at random, and define the random variable D as the deference between
their scores. We can assume that their scores are independent.
Find the probability that their scores are within 10 points of each other
You may round your answer to two decimal places
P (|D| < 10) ≈

, 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