00:01
Assume that 14 % of people are left -handed.
00:03
Suppose 10 people are selected at random.
00:06
Answer each question about right -handers below.
00:09
Now notice this is focused on right -handers, but our proportion is given to us for left -handers.
00:14
So when we're calculating this proportion, we're going to want to take 1 -1 -point -1 -4 to figure out the proportion for right -handers.
00:22
So we're going to assume that this is a binomial, and we're not going to let our mind circle around.
00:28
What if they're ambidextrous or some other thing like that? that, then we're going to assume that they're either right or left -handed.
00:35
So our proportion is 0 .86.
00:37
We have 10 people.
00:39
So n equals 10.
00:40
So part a, find the mean and standard deviation of the number of right -handers in this group.
00:47
So our mean is n times p, and that would be 8 .6.
00:55
And our standard deviation would be the square root of n times p times 1 minus p, which would be 1 .097.
01:10
What's the the probability that they're not all right -handed.
01:14
That's a little bit, i think, tricky wording.
01:18
But really what we're looking for if we take that exactly as it said is that one minus the probability that all 10 of them are right -handed.
01:30
So we would take one minus 10 combination 10 times 0 .86 to the 10th power times 0 .14 to the 0 .0 power.
01:46
And that would equal for us 1 minus 0 .2 to 1 for a probability of 0 .779.
02:02
What's the probability that there are no more than 9 righties? so the probability that x is less than or equal to 9, it's going to be the same as what we found up above...