Details According to the US Census, 30% of the population of...

Details According to the US Census, 30% of the population of Idaho have a bachelor's degree or higher. If 5 people are randomly selected in Idaho, find the probability that ... (Round the answers to 4 decimal places.) a) ... all of them have a bachelor's degree or higher: b) ... 2 of them have a bachelor's degree or higher: c) ... at most 4 have a bachelor's degree or higher:

Transcript

00:01 Our question says, according to the united states centers, about 30 % of idaho residents live in metropolitan areas.

00:07 This percentage is the lowest among 50 states in the nation.

00:11 A catalog sales company in georgia purchased a list of all hidaho consumers.

00:16 The company's marketing analysis selected 25 random sample from the list.

00:21 So the first question says, what is the probability that no more than eight of these people live in metropolitan areas? the question b says that what is the probability that the analyst will be? find more than 10 people 10 of the people in the sample live in the metropolitan areas and question 6 says that what is the probability that at least five people live in metropolitan area so first in first let's extract out our details according to the united states census 30 percent of idaho residents lived in metropolitan area so that means our population proportion p is actually equals to 30 percent and that's 0 .3 so our question went on to say that this percentage is the lowest among the 50 states in the nation a catalog sales company in georgia purchased a list of idaho consumers the company marketing analysis selected 25 random samples so our sample size n is equals to 25 so yes where the question comes inside so the first question says what is the probability that no more than eight people out of this 25 live in metropolitan area so that means a first question probably that's not more than 8 x is later than when equal to 8 out of 25 8 out of 25 lives in the metropolitan area so this simply implies that 8 out of 25 we have to get the sample proportion so if n is equal to 25 and x bar is the number of people that live in in the metropolitan area then the sample proportion pickup is going to be 8 divided by 25 and when we do the math 8x divided by 25 that gives us 0 .32 so that means you're looking for the proportion at least that the proportion is at most 0 .3 so this is what we're trying to get so we can say that probability that x is less than or equal to 8 same thing as saying probability that p cap is lesser than or equals to 0 .32 so to get this value we have to standardize it by using the formula that says that z is equal to p cap minus p divided by the square root of p times q divided by n a pickup in this case is actually 0 .32 minus p is a 0 .3 divided by the square root of p is our 0 .3 times q is 1 minus p that 1 minus 0 .3 that gives us 0 .7 divided by and our n is 25 so 0 .3 to minus 0 .3 that gives us 0 .0 .02 divided by so let's use a calculator 0 .3 times 0 .7 divided by 25 that gives us 0 .09165 and when we do the math we have a 0 .0 .02 divided by 0 .0965 we have that to be 0 .265 we have that to be 0 .2 so we have a probability that pick up is less than 0 .32 to be the same thing as probability that z less than a equals 0 .22 so let's use your calculator to get this value i'll be using a calculator to get this probabilistic value over here so here's my calculator our test is pointing towards the left we have a z score and our z score is uh 0 .2 and as you can see the p value is 0 .5871 so this is a 0 .5871 so this is a 0 .5 so the probability that no more than eight of these people live in the metropolitan area is actually 0 .5874.

04:05 Question 2 states that what is the probability that the analyst will find more than 10 people live in this metropolitan area.

04:14 So in this case of us, our x in this case is equal to 10.

04:18 N still remains 25.

04:20 So that means our sample proportion pick up is equals to 10 over 25...

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