00:01
A poll reported that 61 % of adults were satisfied with the job of major airlines, and we are going to suppose 20 adults are selected at random, and the number who are satisfied is recorded.
00:21
So this is going to be binomial probability because there's a fixed number of trials.
00:39
We're going to count successes out of the 20 adult.
00:42
That we selected at random.
00:45
The trials are independent.
00:54
When we ask one adult whether they were satisfied with the job the major airlines were doing, the response should not be impacting any other responses from other members or participants in the survey.
01:10
There's only two outcomes.
01:16
Either yes, they were satisfied with the job or no, they were not.
01:20
And because it meets all those criteria, then the probability of x successes is equal to ncx times p to the x times q to the n minus x.
01:39
And q is equivalent to 1 minus p.
01:43
So therefore, q would be 1 minus 1 .61 or 0 .39.
01:52
So in part a, we want to determine the probability.
01:59
That exactly 11 of the 20 say that they are satisfied with the job of the major airlines.
02:07
So what we're going to do is we're going to apply our formula and is 20 c11, multiplied by p, which is 0 .61, to the x or 11th power, multiplied by q, which is 0 .39, raised to the 20 minus 11 power.
02:29
And that is going to yield a probability of 0 .152 -55116, and your directions were very clear to round to four decimal places.
02:42
In part b, we want to determine the probability that at least 14 are satisfied.
02:51
So at least 14 is greater than or equal to 14.
02:55
So in order to do this one, i would look at the probability distribution.
03:00
Or at least the part of the probability distribution, where x is greater than are equal to 14.
03:06
So x could be that 14 out of the 20 are satisfied, or 15 or 16, or 17, or 18, or 19, or 20.
03:18
So that means we're applying this formula seven different times, and each time we're changing just the value of x.
03:29
So the first time we use that formula, we're letting x be 14, and we get a probability of 0 .134 -706 -6 -6701...