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Final Review: Normal Distribution Probability Problems and Study Tips

This chapter provides a comprehensive review of probability problems involving normally distributed thermometer readings with a mean of 0°C and standard deviation of 1°C. The problems range from calculating probabilities for specific temperature ranges to working with standard normal distribution and z-scores. Students are encouraged to draw sketches for visual understanding and practice various problems to enhance their grasp of the material. Additionally, study tips are included, encouraging extra practice with the provided chapter review guide to prepare effectively for finals.

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Final Review: Normal Distribution Probability Problems and Study Tips

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  1. Chapter 6 Final Review CPS

  2. Problem #1 - Demo • Assume that thermometer readings are normally distributed with a mean of 0ᵒC and a standard deviation of 1ᵒC. Draw a sketch and find the probability of the reading. Less than -2.75 0.0030

  3. Problem #2 - Demo • Assume that thermometer readings are normally distributed with a mean of 0ᵒC and a standard deviation of 1ᵒC. Draw a sketch and find the probability of the reading. Greater than 2.33 0.0099

  4. Problem #3 - Demo • Assume that thermometer readings are normally distributed with a mean of 0ᵒC and a standard deviation of 1ᵒC. Draw a sketch and find the probability of the reading. Between -2.87 and 1.34 0.9078

  5. Problem #4 – Your Turn! • Assume that thermometer readings are normally distributed with a mean of 0ᵒC and a standard deviation of 1ᵒC. Draw a sketch and find the probability of the reading. Between -4.50 and 1.00 0.8412

  6. Problem #5 – Your Turn! • Assume that thermometer readings are normally distributed with a mean of 0ᵒC and a standard deviation of 1ᵒC. Draw a sketch and find the probability of the reading. Greater than -1.75 0.9599

  7. Problem #6 - Demo • The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 0.1075 1.24

  8. Problem #7 – Your Turn! • The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 0.9418 -1.57

  9. Problem #8 - Demo • Find the indicated value. z0.02 2.05

  10. Problem #8 – Your Turn! • Find the indicated value. z0.005 2.575

  11. Problem #9 - Demo • The Gulfstream 100 is an executive jet that seats six, and it has a doorway height of 51.6 inches. What percentage of adult men can fit through the door without bending given that men’s heights are normally distributed with a mean of 69 in. and a standard deviation of 2.8 in.? z score: 0.0001 Percentage: 0.01%

  12. Problem #10 – Your Turn! • The Gulfstream 100 is an executive jet that seats six, and it has a doorway height of 51.6 inches. What doorway height would allow 60% of men to fit without bending given that men’s heights are normally distributed with a mean of 69 in. and a standard deviation of 2.8 in.? 69.7 inches

  13. Study Tips • Extra Practice Recommendation: Print off the Chapter 6 Review Guide. Practice any problem that you would struggle with if it was on the final.

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