Probability Problem: Mean 100, Directions 550,000, 295,456, ✓ Solved

Prb3mean100directions5500002954566stdev15find The Probabilities

Find the probabilities given X values:

1. Probability of IQ less than 56.5 points, use 4 decimal places.

2. Probability of IQ less than 59.5 points, use 4 decimal places.

3. Probability of IQ less than 62.5 points, use 4 decimal places.

4. Probability of IQ less than 68.5 points, use 4 decimal places.

5. Probability of IQ less than 74.5 points, use 4 decimal places.

6. Probability of IQ less than 80.5 points, use 4 decimal places.

7. Probability of IQ less than 86.5 points, use 4 decimal places.

8. Probability of IQ greater than 56.5 points, use 4 decimal places.

9. Probability of IQ greater than 59.5 points, use 4 decimal places.

10. Probability of IQ greater than 62.5 points, use 4 decimal places.

11. Probability of IQ greater than 68.5 points, use 4 decimal places.

12. Probability of IQ greater than 74.5 points, use 4 decimal places.

13. Probability of IQ greater than 80.5 points, use 4 decimal places.

14. Probability of IQ greater than 86.5 points, use 4 decimal places.

15. Probability of IQ between 70 and 74.5 points, use 4 decimal places.

16. Probability of IQ between 100 and 110 points, use 4 decimal places.

17. Probability of IQ between 110 and 118 points, use 4 decimal places.

18. Probability of IQ between 118 and 125 points, use 4 decimal places.

Source: Essentials of Statistics by Mario Triola

Paper For Above Instructions

In statistics, we often use normal distribution to describe the behavior of a population under certain assumptions, primarily when variables are measured along an interval. Calculating probabilities for IQ scores is a common exercise in understanding and applying this important concept. For this case, we have a mean (μ) of 100 and a standard deviation (σ) of 15.

To compute the probabilities accurately for the various IQ score thresholds provided, we will use the cumulative distribution function (CDF) for the normal distribution, denoted as NORMDIST in Excel. The formula used for calculating the probability density function in the context of normal distribution is:

P(X ≤ x) = NORMDIST(x, μ, σ, TRUE)

We will analyze probabilities based on the provided IQ thresholds.

1. Probability of IQ less than 56.5 points

Using the formula:

P(X

2. Probability of IQ less than 59.5 points

P(X

3. Probability of IQ less than 62.5 points

P(X

4. Probability of IQ less than 68.5 points

P(X

5. Probability of IQ less than 74.5 points

P(X

6. Probability of IQ less than 80.5 points

P(X

7. Probability of IQ less than 86.5 points

P(X

8. Probability of IQ greater than 56.5 points

P(X > 56.5) = 1 - P(X

9. Probability of IQ greater than 59.5 points

P(X > 59.5) = 1 - P(X

10. Probability of IQ greater than 62.5 points

P(X > 62.5) = 1 - P(X

11. Probability of IQ greater than 68.5 points

P(X > 68.5) = 1 - P(X

12. Probability of IQ greater than 74.5 points

P(X > 74.5) = 1 - P(X

13. Probability of IQ greater than 80.5 points

P(X > 80.5) = 1 - P(X

14. Probability of IQ greater than 86.5 points

P(X > 86.5) = 1 - P(X

15. Probability of IQ between 70 and 74.5 points

P(70

16. Probability of IQ between 100 and 110 points

P(100

17. Probability of IQ between 110 and 118 points

P(110

18. Probability of IQ between 118 and 125 points

P(118

Conclusion

This analysis provides a foundational understanding of how normal distributions can be utilized to derive probabilities related to IQ scores. These values help in assessing performance in relation to general population norms. This can be applied in various fields including education, psychology, and more.

References

  • Triola, M. F. (2018). Essentials of Statistics. Pearson.
  • Bluman, A. G. (2018). Elementary Statistics: A Step by Step Approach. McGraw-Hill.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2016). Introduction to the Practice of Statistics. W.H. Freeman.
  • Newman, D. J. (2018). Probability and Statistics. Academic Press.
  • Scheaffer, R. L., & McClave, J. T. (2016). Statistics. Cengage Learning.
  • Ghasemi, A., & Zahediasl, S. (2012). Normality Tests for Statistical Analysis: A Guide for Non-Statisticians. International Journal of Endocrinology and Metabolism, 10(2), 494-496.
  • Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics. SAGE Publications.
  • Weiss, N. A. (2017). Introductory Statistics. Pearson.
  • Wackerly, D. D., Mendenhall, W., & Scheaffer, L. (2014). Mathematical Statistics with Applications. Cengage Learning.
  • Utts, J. M. (2015). Seeing Through Statistics. Cengage Learning.

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