Constructing Normal Quantile Plots. In Exercises 17–20, use th...

Question

Constructing Normal Quantile Plots. In Exercises 17–20, use the given data values to identify the corresponding z scores that are used for a normal quantile plot, then identify the coordinates of each point in the normal quantile plot. Construct the normal quantile plot, then determine whether the data appear to be from a population with a normal distribution.

Earthquake Depths A sample of depths (km) of earthquakes is obtained from Data Set 24 “Earthquakes” in Appendix B: 17.3, 7.0, 7.0, 7.0, 8.1, 6.8.

Earthquake Depths A sample of depths (km) of earthquakes is obtained from Data Set 24 “Earthquakes” in Appendix B: 17.3, 7.0, 7.0, 7.0, 8.1, 6.8.

Accepted Answer

Hello everyone. Let's take a look at this question together. A sample of weights in kilograms of newborn babies is as follows 2.965, 3.150, 3.363, 3.490, 3.674, and 5.291. For these data values, identify the corresponding Z scores used for a normal quantile plot, then list the coordinates of each point in the normal quantile plot. Does the data appear to be from a population with a normal distribution? So the first step in solving this problem is to order the data from smallest to largest. So we have our ordered data with the weights of the newborn babies from smallest to largest. And then we assign each data value a rank represented by the letter I from 1 to 6. So our ranks are the values of 12345, and 6, and then we can calculate the percentile for each data value using the formula P sub 1 is equal to i minus 0.5 divided by N. Where the variable n is equal to 6 and we know that the variable I represents our rank, so then we compute the formula for each of the following ranks, for I equals 12345, and 6, giving us the following values for P1, we have 0.083, E2, we 0.250.3, we have 0.417. P4 0.583. P5 is 0.750, and P6 is equal to 0.917. And then we can find the Z scores corresponding to each cumulative probability using the standard normal distribution table. So for our P1 value, our Z score is approximately -1.385. For P2, our Z score is approximately 0.674. P3, our Z score is approximately 0.210. P4, our Z score is approximately 0.210. P5, our Z score is approximately. 0.674 and P6 our Z score is approximately 1.385. And then using our Z score and our percentile, we can list the different coordinates, which is ordered from Z score and data value, and it gives us the following coordinates for the normal quantile plot. And using the coordinates, we can then Assess normality based on the plot in which the first five points, which are up to 3.674 kg, are fairly linear, but the last point, which is 5.291 kg, is much higher than expected, indicating a possible outlier. And so this suggests that the data may not be perfectly normal due to the high. Value at the upper end. And so looking at our answer choices, we can identify the answer choice containing the correct Z scores and the coordinates of each point in the normal quantile plot is answer choice B, and answer choice B also says that the data does not appear to be from a population with a normal distribution, so answer choice B is correct. And all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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Key Concepts

Z-scores

Normal Quantile Plot

Normal Distribution

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