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1 Expert Answer Using a normal distribution table, it can be found that P(80 < z) = . 5 (this is the probability that a random score would be greater than 80. It makes sense that it is . 5 or 50% because 80 is the mean.)
Results of zero show the point and the mean equal. A result of one indicates the point is one standard deviation above the mean and when data points are below the mean, the Z-score is negative.
We know from part b that the percentage from 65 to 75 is 47.5%.
the empirical rule is 68-95-99 or roughly 68% within one standard deviation of the mean, 95% within two, and 99% within 3. 80% be somewhere between 1 and 2 standard deviations from the mean.
We know from part b that the percentage from 65 to 75 is 47.5%.
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People also ask

From the graph we can see that 68% of the students had scores between 70 and 80. For this problem we need a bit of math. If you looked at the entire curve, you would say that 100% of all of the test scores fall under it.
The critical z-score values when using a 95 percent confidence level are -1.96 and +1.96 standard deviations.
6:04 7:54 We need to find the area on the right. This small area here. So again we'll first find theMoreWe need to find the area on the right. This small area here. So again we'll first find the probability that x is greater than 135.
Using the standard deviation, statisticians may determine if the data has a normal curve or other mathematical relationship. If the data behaves in a normal curve, then 68% of the data points will fall within one standard deviation of the average, or mean, data point.
Fun fact: the percentage of our distribution that falls in a given area is exactly the same as the probability that any single observation will fall in that area. In other words, we know that approximately 34 percent of our data will fall between the mean and one standard deviation above the mean.

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