Examples of NSC 68 in the following topics:
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The Military Implementation of Containment
- In his autobiography, President Truman acknowledged that fighting the invasion was essential to the American goal of the global containment of communism as outlined in the National Security Council Report 68 (NSC-68).
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Containment
- Completed in April 1950, it became known as NSC 68.
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Containment in Foreign Policy
- Truman approved a classified statement of containment policy called NSC 20/4 in November 1948, the first comprehensive statement of security policy ever created by the United States.
- Completed in April 1950, it became known as NSC 68.
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Working Backwards to Find the Error Bound or Sample Mean
- We may know that the sample mean is 68.
- If we know that the sample mean is 68: EBM = 68.82 − 68 = 0.82
- If we don't know the sample mean: EBM = (68.82 − 67.18)/2 = 0.82
- If we know the error bound: = 68.82 − 0.82 = 68
- If we don't know the error bound: = (67.18 + 68.82)/2 = 68
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Changing the Confidence Level or Sample Size
- We estimate with 95 % confidence that the true population mean for all statistics exam scores is between 67.02 and 68.98.
- The 90% confidence interval is (67.18, 68.82).
- The 95% confidence interval is (67.02, 68.98).
- x = 68• σ = 3 ; The confidence level is 90% (CL=0.90) ; = z = 1.645
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Confidence Interval for a Population Mean, Standard Deviation Known
- A random sample of 36 scores is taken and gives a sample mean (sample mean score) of 68.
- $\bar { x } =68 \\ \sigma =3 \\ n=36 \\ \text{ME}={ z }_{ \frac { \alpha }{ 2 } }\left( \dfrac { \sigma }{ \sqrt { n } } \right)$
- $\displaystyle {\text{ME} = 1.645\cdot \frac{3}{\sqrt{36}} = 0.8225 \\ \bar{x} - \text{ME} = 68-0.8225 = 67.1775 \\ \bar{x} + \text{ME} = 68+0.8225 = 68.8225}$
- The 90% confidence interval for the mean score is $(67.1775, 68.8225)$.
- In conclusion, we are 90% confident that the interval from 67.1775 to 68.8225 contains the true mean score of all the statistics exams. 90% of all confidence intervals constructed in this way contain the true mean statistics exam score.
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Areas Under Normal Distributions
- The shaded area between 40 and 60 contains 68% of the distribution.
- As in Figure 1, 68% of the distribution is within one standard deviation of the mean.
- The normal distributions shown in Figures 1 and 2 are specific examples of the general rule that 68% of the area of any normal distribution is within one standard deviation of the mean.
- Normal distribution with a mean of 100 and standard deviation of 20. 68% of the area is within one standard deviation (20) of the mean (100)
- Normal distribution with a mean of 50 and standard deviation of 10. 68% of the area is within one standard deviation (10) of the mean (50).
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68-95-99.7 rule
- Use the Z table to confirm that about 68%, 95%, and 99.7% of observations fall within 1, 2, and 3, standard deviations of the mean in the normal distribution, respectively.
- For instance, first find the area that falls between Z = −1 and Z = 1, which should have an area of about 0.68.
- Next verify the area between Z = −1 and Z = 1 is about 0.68.
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The Blues Scale
- (Some versions are pentatonic. ) Rearrange the pentatonic scale in Figure 4.68 above so that it begins on the C, and add an F sharp in between the F and G, and you have a commonly used version of the blues scale.
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Median and Mean
- Table 1 shows the absolute and squared deviations of the numbers 2, 3, 4, 9, and 16 from their median of 4 and their mean of 6.8.
- Figure 1 shows that the distribution balances at the mean of 6.8 and not at the median of 4.
- Absolute and squared deviations from the median of 4 and the mean of 6.8
- The distribution balances at the mean of 6.8 and not at the median of 4.0