00:01
In this exercise, we are told that 85 % of students say they do not get enough sleep.
00:06
So that means for a given student, the probability that the student says he or she does not get enough sleep is 0 .85.
00:13
And we have a random survey of 22 students.
00:18
And so we were asked to find the probability that exactly 20 of them say they do not get enough sleep.
00:25
So let's let x be the random variable that is the number that say they do not get enough sleep.
00:40
So here x is a binomial random variable.
00:50
Binomial has two parameters.
00:52
P is the probability of success and n is the number of trials.
00:57
So we're looking for the probability that x is equal to exactly 20.
01:03
The probability mass function for the binomial random variable is given by this formula.
01:11
It's n choose x times p to the exponent x times 1 minus p to the exponent n minus x, where x can be any integer value from 0 up to n.
01:26
So here this is equal to 22 choose 20 times 0 .85 to the exponent 20 times 0 .15 to the exponent 2.
01:42
And this comes out to a probability of approximately 0 .2015...