Determining Normality. In Exercises 9–12, refer to the indicat...

Question

Determining Normality. In Exercises 9–12, refer to the indicated sample data and determine whether they appear to be from a population with a normal distribution. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a distribution that is roughly bell-shaped.

Dunkin’ Donuts The drive-through service times (seconds) of Dunkin’ Donuts lunch customers, as listed in Data Set 36 “Fast Food” in Appendix B

Dunkin’ Donuts The drive-through service times (seconds) of Dunkin’ Donuts lunch customers, as listed in Data Set 36 “Fast Food” in Appendix B

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A sample of 25 exam scores from a statistics class is as follows. 72,757880818385 86, 87888989,9091, 92,93, 9495. 96, 97, 9899, 100, 100. 100. Based on the distribution of these scores, does the data appear to be from a population with a normal distribution? Awesome, so it appears for this particular prompt, we're asked to take. Our information that is provided to us by the prom itself. So based on the distribution of these particular exam scores, does the data appear to be in the appear to be in a normal distribution pattern for this population? So is the population with a normal distribution. That is what we're ultimately trying to solve for. So with that said, let's take a moment to read off our multiple choice answers to see what our final answer might be. A is the data is left skewed with a cluster of high scores, so it is not normal. B is the data is right skewed with most scores low, so it is not normal. C is the data is roughly bell shaped and symmetric, so it is likely normal, and finally D is the data is bimodal with two distinct peats. Peak, so it is not normal. So with that said, our first step is we need to arrange our scores in order. So when we arrange our scores in order, So when we arrange our data points in order, rather I should say, specifically the exam scores in numerical order, we will receive the following. So in numerical order we have 72, 75, 78, 80, 81 83 85 8687, 88 89 89 90, 91 92 93 94 95 96 97 98 99 100, 100, 100. And as you can see, looking at this grouping of values, we should be able to note that there is a cluster of high scores at the upper end with 3 scores of 100, and the lower scores are the most spread out. Therefore, this means that the mean is calculated as 2000. 238 divided by 25, which will be equal to 89.52. So the median is the 13th value, which is 90. So the mean is lower than the median, which means that there will indicate that there is left skewness. Which that means therefore, as a result, the data is not symmetric and has a cluster of high values, so it does not appear to come from a normal distribution. So therefore, without a doubt, our final answer has to be multiple choice. Answer letter A, which once again is the data is left skewed with a cluster of high scores, so it is not normal. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Normal Distribution

Central Limit Theorem

Normality Tests

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