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The average length of crocodiles in a swamp is 11.65 feet. If the standard deviation of 3 feet; find the probability lengths are normally distributed with that a c...

Question

The average length of crocodiles in a swamp is 11.65 feet. If the standard deviation of 3 feet; find the probability lengths are normally distributed with that a crocodile is more than 12 feet long:0.4980.2940.3740.453

The average length of crocodiles in a swamp is 11.65 feet. If the standard deviation of 3 feet; find the probability lengths are normally distributed with that a crocodile is more than 12 feet long: 0.498 0.294 0.374 0.453



Answers

The Old Farmer’s Almanac reports that the average person uses 123 gallons of water daily. If the standard deviation is 21 gallons, find the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons. Assume the variable is normally distributed.

Based on this problem, we know that a cell phone has a lifetime average of being 24.3 months with a standard deviation of 2.6 months. And this is information dealing with the population of cell phones. And in this problem, the company is going to provide 33 employees with the cell phone. So, in essence, we're drawing a sample of cell phones from this population with the 33 cell phones, and the question is asking us what is the probability, or find the probability that they mean, which is the X bar is less than 23.8 months. So because we're talking about a sample of 33 people getting cell phones and we want the distribution of the average of those cell phones were going to apply the central Limit Theorem and the Central Limit Theorem says that the average of the means is the same as the average of the population, which is 24.3, and the standard error of the mean, or the standard deviation of the means is the same as the standard deviation of the population divided by the square root of end. So that's in this case going to be a 2.6 divided by the square root of 33. So we're going to want to draw an image, a bell shaped curve to reflect the problem. And we always put our average in the center and are averages 24.3. And the problem is asking us about being less than 23.8. So we're talking 23.8 right here, and we want to go less than so. The next thing we're gonna need to do is we're going to need to find the Z score associated with 23.8. So the Z score would be 23.8 minus 24.3, divided by standard error of the mean We should be 2.6 over the square root of 33 and the Z score turns out to be approximately negative 1.10 So the 23.8 is negative 1.10 meaning it's 1.10 standard deviations below the mean. So what we can do is we can rewrite this problem instead of talking in terms of the X score we can say that the probability that the averages less than 23.8 is no different than the probability that the Z score is less than negative 1.10 And at that point we would go to the standard normal distribution table in the back of your textbook and the probability that the Z is less than negative 1.10 is 0.13 57 So, to recap, our answer. The question waas that if we give cellphones to 33 people, what is the probability that the average of those 33 cell phone less less than 23.8 months and your answer be 0.1357?

I Our problem Number 75 is, um, stating that we have a length in INGE off cricket and it is a random variable X with me in 1.2 inch and standard deviation off open to fire. And the question here is asking around the median and the standard deviation off another random variable. Why? Where? Why is in centimeters and X is an inch where and 2.54 centimeters it will one inch. So let's start our answer by stating the givens they give it the year is the mean off Rundle. Very relax and standard deviation off bendable run the very real X. The mean off random variable X is 1.2, and the son of the Asian off random variable X is open to five. So first this year, rights that the mean is 1.2 and the sender division is old 0.2. Fine. Now we are searching for that. Me and the Senate Aviation off run the very world war where why is equal, as we say, two 0.5 for X, because one inch is equal to 2.54 centimeters by using the property's off meaning the standard deviation. We can say that you or a X plus B is equal to a month the blind by new backs plus p. So we can use this equation by saying that why is equal to a which is 2.54 x plus be, which is equal to be here is equal to zero. So here we can say that a is equal to two point fine four month of flying by knew of X, which is equal to what's going to right. So the answer will be, ah, one going to must blind by 2.45 which is equal to three coins for eight, the same thing we can use here. The property's off the Sunda deviation, which say that the son of the agent off explodes. B is equal to a multi blind by the standard deviation of acts as we know here that a is equal to 2.54 and the standard deviation of axes open to five. So to send that deviation off, why is equal to a which is to point 54 multiplying by some of the divisional acts, which is all points 25 so the final answer would be 2.5 formative blind by opening fire sorties. Oh, point. Thanks, Thio. Fine. Right. Thank you.

Problem Number 75 um, as we know that since one inch is equal toe 0.5 boys and teenagers, So why is equal to two point crying for, uh, X and eso? We can't find that in Ah, or that mean off Roy is equal to Ah, you mean off 2.5 for X which is equal toe 0.5 for multiplying by 1.2 to the front answer would be 3.0 for for eight. Ah, standard deviation. It's under division off the boy is people to standard deviation off 2.54 I fight for X, but she's even toe for multiplying by opening to crime. Oh, jeez. Open toe 00.6363 If I, ah, 1.2 if the mean for it I mean for X which is given and the means of wrecks in Quito we took and standard revision backs is equal to ah all going through

No result this problem. You are going to need a calculator that has what we call a normal CDF function on it. More than likely, that will need to be a graphing calculator If you have one. There are online calculators available. Simply go to Google or some other search engine and type in online calculator with normal CDF, and it should bring up something online that you can use. Um, once you find that there's gonna be four pieces of information that you need to give that calculator so that it can calculate this probability for you, it's going to need you to give it low. The high, the mean and the standard deviation, mean and standard deviation of brought me the first things you guys were given. Ah, in this case, were given a mean of six and a standard deviation of three. Okay, and then it's asking us to find the probability for when X is between two and seven, right? That's what that compound inequality is saying to is less than or equal to X is less than or equal to seven. That's meaning that's asking for what's the probability? Whenever X is between two and seven. So too would certainly be your low as the lower number. And seven would certainly be your high as the higher number. I don't know why I just read that backwards. I'm sorry too. Seven. There we go. Make sure if you're using you can clear that you are plucking them incorrectly. Okay. Meaning I'm I listed the order than most calculators taken. Obviously, I can't promise every single calculator is exactly the same way, so make sure you check yours. But most calculators should be asking you in the order of low high, mean and standard deviation. If you plug it all in correctly, you should get back from your calculator. A probability of zero point 5393 or somewhere around there, depending on how many digits. Okay, we are asked around to the hundreds place. So that means for us we would round that up to a 0.54 as our probability


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