00:01
For this problem, we are told to suppose that exactly 10 % of students at su are left -handed.
00:06
We select 15 students at random from the school and define w equals the number who are left -handed.
00:13
For part a, we're asked to find the probability that exactly three students in the sample are left -handed.
00:18
So this is going to be probability x equals 3 in the form of a binomial experiment.
00:26
So that is going to be equal to 15, choose, times the probability of getting a left -handed student to the power of three times the probability of getting a non -left -handed student to the power of 15 minus 3, which is 12.
00:44
So binomial 15 -3 is my way of writing 15 -3 here.
00:50
We have 0 .1 cubed, 0 .9 of 12.
00:55
So we have that probability is going to be equal to 0 .185, roughly.
01:04
Then for part b, we're as to find the probability that the number of left -handed students in the sample are between 1 and 5 inclusive.
01:11
So that's probability that 1 is less than or equal to x, less than or equal to 5, which will be equal to the sum from, we'll call it j equals 1 up to 5, of 15 choose j from 0 .1 to the power of j times 0 .9 to the power of 15 minus j so actually do it this way we can do some binomial 15 choose j 0 .1 to the power of j in minus j j j from 1 to 5 so we find that probability is going to be equal to 0 .792, roughly.
02:08
For part c, we're as to find the probability that you select fewer than four left -handed students...