You first simplify
tan(x) = cos(x)/sin(x) and cot(x) = sin(x)/cos(x)
Then you plug that in and then you simplify even more
We have been given that a set of art exam scores are normally distributed with a mean of 81 points and a standard deviation of 10 points. Kamil got a score of 78 points on the exam. We are asked to find the proportion of exam scores that are lower than Kamil's score.
First of all, we will find z-score corresponding to 78.
, where,
z = z-score,
x = Random sample score,
= Mean,
= Standard deviation.
Now we will use normal distribution table to find the probability under a z-score of that is .
Upon rounding to 4 decimal places, we will get:
Therefore, of exam scores are lower than Kamil's score.
105/1000 is the answer :)