00:01
And this question, you were given that in 2016, the better business bureau set out 75 % of the complaints that received in the united states, right? now, suppose you have been hired by this bureau to investigate the complaint that received this year involving new car dealers, and you plan to select a sample of 200 new car dealers, right? and, i mean, 200 new car dealer complaints, right? estimate the proportion of complaints, right? now, assume the proportion of the population proportional of the population of the compliance set for new cardilla is the same as the overall proportioned in 2016, that is 75%.
00:42
So you asked the first question, so first you select the sample of 200 new card dealers, right? so what is the sampling distribution, right? the sample of the speech first has a mean, right? the mean, of course, is the same as the population means 75 %, right? so what is the sample standard deviation for the, what is the standard deviation of the sampling mean, right, proportion, right? that's of course given by the square root of 75 % times of 1 minus 75%, that's 25 % and divided by the sample size 200, right? so you'll find this, of course, to be given by, if we do the calculation, you will find this to be actually given by square three over, square three over 20, right? so you'll find this to be given by square of three over 20.
01:39
And i found this to be actually given by 0 .09.
01:45
So that's the standard deviation.
01:48
And the second question is based on this sample of 200 complaints, what's probably that the sample proportion will be within will be within actually 6 % of the population proportion, right? so you talk about 6 % of population proportion.
02:06
That means the d score actually is, you know, the d score is going to be actually given by, you know, 0 .06 over 0 .09, right? so you'll find this, this score to be actually given by, so 6 over 9, right? so 6 divided by 9, that of course gives you, 0 .67, right? now, if you look up, if you ask the probability, if you ask the probability of, you know, the sampling me line within this 0 .006 from the mean, and that of course is given by 1 minus 2 alpha, right? now, alpha you can find from the score, right? so the alpha, you said this, the the square alpha equals 0 .67.
02:52
And you look up your z table, you'll find that this, that's actually gives you a 25%, 25 .1%, right? so you'll find this out of actually is 25 .14%.
03:08
And of course, the probability, therefore, it's given by 1 minus there.
03:15
So that's actually 1 minus 50 .28%.
03:19
So you get actually 49 .72%.
03:23
So that would be the probability...