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Probability and Normal Distribution Calculations: Thermometer Readings and Men's Heights

This document presents a series of probability problems based on normally distributed thermometer readings with a mean of 0°C and a standard deviation of 1°C. It includes visual representations of the distributions and calculations for probabilities of readings falling below, above, or between specified values. Additionally, it addresses men's height distribution relative to an executive jet's doorway height, determining the percentage of men that can pass through the doorway without bending and calculating the necessary height to accommodate a specific percentage.

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Probability and Normal Distribution Calculations: Thermometer Readings and Men's Heights

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  1. 6.2-6.3 Whiteboards Review CPS

  2. Problem #1 • 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 • 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 • 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 • 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 • 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 • The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 0.1075 1.24

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

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

  10. Problem #9 • 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%

  11. Problem #10 • 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

  12. Homework • Complete review guideexcept for #13.

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