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A set of 250 data values is normally distributed with a mean of 50 and a standard deviation of 5.5

What is the probability that a data value selected at random is greater than 39$?$

97.7$\%$

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Campbell University

Oregon State University

Baylor University

Idaho State University

so put the top of the screen here. You can see I've got a generic normal distribution drawn out here where the mean is in the center of the graph. And I've got the 1st 2nd and third standard deviations marked out here along with their percentages, because we know that 68% assuming that data is normally distributed. We know that 68% of our data is one standard deviation from the mean the 95% of our data's two standard deviations from the mean and 99% of our data's three standard deviations from the mean this is stuff that was covered in 12-7. That's why it's in the review section. So this is with a little bit of assumption that you've done that already. Um, but assuming the chicken with how that all breaks down, assuming you've learned that before, then we can just go ahead and have a written and move on down here, gone ahead and drawn out a normal distribution for this specific problem because it tells us for the specific problem that we have a mean of 50. So I'm mark to that on the black line and we know that our standard deviation is 5.5. So I went ahead and added 5.53 times and subtracted 5.53 times so that we've got our first, second and third standard deviations marked out here. Now the actual question is asking us to find the probability that we would select something at random greater than 39 meaning, it's saying from here 39 all the way to the right. It wants to know how much what percent of the graph, what percent of the data is that? Okay, Well, all we need to do is look at our generic normal distribution. Appear if we look at 39. 39 is the red line meaning we're talking about from here to the right. So all I need to do all we need to do is just add up all of those percentages. Meaning we need to take 13.5% right here, plus 34% plus the other 34% plus this 13.5% plus 2% and finally, plus this little 0.5% here. All of those added up will show us the portion of the graph portion of the data that we have here. If we add all of that up, what you get is 97 0.5% and that would be your answer for this problem.

University of Central Missouri