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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

10. Normal Distributions

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Exercise 28 Page 744

To start solving, find the difference between the mean of the data set and the lower bound of the given interval.

97.5 %

Practice makes perfect

We know that the set of data is normally distributed with a mean of 100 and a standard deviation of 10. We will find the probability of choosing a value that is at least 80. x≥ 80 First, let's find the difference between 80 and the mean 100.

80- 100= - 20 Then, we will divide the difference by the standard deviation 10. - 20/10=- 2 Thus, 100 is 2 standard deviations below the mean. To find the probability, we will shade the percent of data which is no more than 2 standard deviations below the mean.

Finally, we can find the percent of data by adding the percents of the shaded areas.

p=13.5 %+34 %+34 %+13.5 %+2.35 %+0.15 %

Add terms

p=97.5 %

The probability of choosing a random value that is at least 80 is equal to 97.5 %.

Subchapter links

Lesson Check p.743

Practice and Problem-Solving Exercises p.743-745

Standardized Test Prep p.745

Mixed Review p.745