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Suppose that the shelf life, the number of days product is on a store's shelf, for 1- gallon cartons of milk is a random variable with Unif [1, 7] distribution...

Question

Suppose that the shelf life, the number of days product is on a store's shelf, for 1- gallon cartons of milk is a random variable with Unif [1, 7] distribution: If a store puts out 100 cartons of 1-gallon of milk for sale, find the probability that the average number of days the cartons remain on the shelf exceeds 4.5 days.

Suppose that the shelf life, the number of days product is on a store's shelf, for 1- gallon cartons of milk is a random variable with Unif [1, 7] distribution: If a store puts out 100 cartons of 1-gallon of milk for sale, find the probability that the average number of days the cartons remain on the shelf exceeds 4.5 days.



Answers

Suppose the mean length of time between submission of a state tax return requesting a refund and the issuance of the refund is 47 days, with standard deviation 6 days. Find the probability that in a sample of 50 returns requesting a refund, the mean such time will be more than 50 days.

This problem explores uniform distributions and it explores probabilities on that uniform distribution. So we're going to start with a completely made of example here, just gonna be similar, let's say we have a uniform uh from 0 to 50 and that means that we know that uniform distributions have to value one over b minus eight, which means that our distribution has the value 1/50 consistently throughout the distribution. That's our value. That's our fx basically. And now let's say that uh the amount of milk dispensed by this boot would be at most 20. So what you want to pay attention to is the freezing and the terms that they use. So at most means that it can be 20 at a maximum. So that means that X our random variable would have to be less than or equal to 20 because we want 20 to be the highest value. So then to solve this were simply just going to integrate from A to B, which is 0 to 50 or rather 0 to 20 here, Right? Because this is our range, so it's either less than 20 and the lowest we can go zero and 20 is the highest we can go here and our value is going to be the same value from 0 to 50 which is just 1/50 dx Yeah, So integrating this out, you would get 20/50 or 2/5. Now, let's see another example, let's say it's more than 25 leaders, but less than 35 m. So here, let's say the probability is 25 less than gold X. Less than or equal to 35. Right? We wanted to be between two values. So we can just integrate between those values and we can look at the function value in those bounds 25 to 35. So this would give us 35 minus 25 is 10 and that's times 1/50. So that just gives us 1/5. Now let's look at a third example, let's say that um it should be at least 40 leaders of right, so now that we're looking at at least 40 at least means that the minimum value it can have is 40 and we already know that the maximum is 50 it can't be more than that. So now we can take our integral from 40 to 50 of the same values before which is just 1/50 this is D. X. Here and you just integrate this out to get your probability which is also 1/5 year. And this is just a different example which you can now use to solve other problems.

79. Supposed that the duration of a particular type of criminal trial is known to be normally distributed with the mean of 21 days in a standard deviation of seven days. A inwards defined the random variable X. So we're gonna let eggs people the link in days of a criminal trial be we want to give that X is a normal distribution that tells us that the mean is 21 says the first thing we insert in the standard deviation of seven. So we'll put that in a second. I see if one of the trials is randomly chosen, find the probability that it lasted at least 24 days in this case and looking for their probability that it lasted at least 24 days, which indicates 24 or more. Okay, because I have a normal distribution center to 21 with standard deviation of seven again. Right out 21 is my center one Senator. Deviation to the right is 28 1 standard deviation to my left before thine. I'm looking for the probability that last more than 24 days Well, shade this into the right, so I know my answer. should be less than 50%. I can insert this into my normal CDF command. So ago, 24 of my lower bound good to infinity, my upper at 21 7 That's what mean center deviation. And I find the probability there's a 0.3341 in de 60% of all trials of this type are completed. And how many days? So this type of problem, what I'm looking for is which value has 60% of the data to the left of it. I still have the same parameters of 21 of seven. So I can use my inversion normal feature my calculator, in which 60% is the area that I'm looking for with the mean of 21 in my standard deviation of seven. And I find 22.77 so I could say approximately 23 days

When this question, we are told that the main number of days to germination is 22. Standard Division is 2.3. This is the population data And were given a sample of 160 seats and were asked for the probability that the mean will be between .5 days. So the sample mean is 22. The sample standard deviation is 2.3 over square root of 1, 16, Which gives us .181". We're going to use the sample mean and standard deviation for our competition. So we're asked for the probability that is point in .5 days. So that texas between 21.5 and 22.5. So that's the probability that are Z values between 2.75 and minus 2.75 which basically gives us 0.997 minus 0.0 three, which is .99.

So this question, we're told that the mean cost of a 30 day supply of the drug is 46.5 ft Standard deviation 4.84 were asked at the probability that the mean, the sample mean of 100 prices Of this drug will be between 45 and 15. So here are sample standard deviation is point for it. Four, Sample means is still the same. So we're going to convert this to our z value, which is 50 minus the mean. Over the sample standard deviation 35- The mean, over sample standard deviation. So that will give us the z value between -3.26 and 7.07. So that's 1 0. Checking there was a funeral funeral. Thanks Just .9994.


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