A recent study of 400 students found that 65% carry calculators. Is this sample large enough to satisfy the Central Limit Theorem conditions of large sample where both the number of successes and number of failures are greater than or equal to 10? So, ultimately, we have two pieces of information given to us. We're given n= 400 students, and that of these 400 students, we were given a proportion p-hat = 0.65. And so, again, what do we want to do? What we want to do is determine if this sample is large enough to satisfy the Central Limit Theorem condition for a large sample. And to satisfy the condition for a large sample, we need to do two things. First, we need to identify what is the success, so you're going to use words, and then you need to count how many successes you have. The second step is you'll need to look at the flip side of the coin; you'll need to identify what is considered a failure. You're going to write that out as words, and then from there, calculate how many failures you'll have. The idea of this second condition, a large sample, is we need both these numbers in blue and purple to be greater than or equal to 10. So let's do each step. It's going to be a three-step process that I've laid out here. Step one: What is considered the success here? That's 65%, representing students who carry calculators. So my success are going to be students who say, "Yeah, I carry a calculator." My success will be students who say, "Yeah, I carry a calculator." So how then do we count how many students carry calculators? Count the number of successes, and we do that by taking the total times the percentage. We take that total of 400 students and multiply that by the percentage that 65% of them say, "Yeah, I carry calculators." 400×0.65. What is that going to equal to? What are the number of students who carry calculator? Perfect, 260. Failure: When you think of the idea of failure, just think of the word "not," alright? So if success is students who carry calculators, failure is "not" students who do not carry calculators. Failure is simply "not." Now, how do you calculate failures? Ultimately, we know 400 students have been surveyed. We know that my sample size is 400 students who've been surveyed, and at this point, we know that the number of successes, those who said, "Yes, I carry a calculator," is 260. So that means everyone else remaining, meaning the remaining 400 students who aren't the 260 students, are students who do not carry calculators. So we take that number of successes, 260, and subtract it from my sample size because what's left then are the number of students who don't carry calculators. How many students are those who do not carry calculators? What's that going to be? Yeah, it's going to be 140. Step one: Calculate your number of successes. Step two: Calculate your number of failures. So step three is checking if the large sample condition is satisfied, and it's satisfied only if both the number of successes and the number of failures are greater than 10. And because both are ultimately satisfied, is the reason why I can say yes, the large sample condition is satisfied. Why? Because both the number of successes as well as the number of failures, they are both greater than 10. That is the only way you could say yes to this large sample condition being satisfied. Why don't you guys try an example? What is the number of successes here? We're looking at 346 nurses, 35 are males. Yeah, number of successes is 121. So then how many are not male? Yeah, 225. Remember, step one: calculate your number of successes. Step two: calculate your number of failures. What about these numbers? What about the number of successes? What about the number of failures? Did I need to be satisfied to satisfy this large sample condition? We need them both to be greater than 10. And so, here's my question then: Is the large sample condition satisfied? Absolutely, and it's because both the number of successes and number of failures are greater than 10.