Download Statistics Chapter 6: Section 6-2: Normal Distribution, Standard

Statistics Chapter 6: Section 6-­2: Normal Distribution, Standard Normal Distribution Normal Distribution Standard Normal Distribution Area & Probability Calculating Areas (probabilities) for variables given a standard normal distribution Normal Distribution: Standard Normal Distribution: BECAUSE THE TOTAL AREA UNDER THE DENSITY CURVE IS EQUAL TO 1, THERE IS A CORRESPONDENCE BETWEEN AREA AND PROBABILITY. THIS MEANS: Finding Probabilities WHEN GIVEN z scores: Remember: Use Table A-­2 About the table: 1. 2. 3. 4. 5. 6. Example: Thermometers are supposed to give readings of 0°C at the freezing point of water. Tests reveal that some thermometers are giving readings above 0°C, and some are giving readings below 0°C. The mean temperature reading is 0°C and the standard deviation is 1.00°C. If the readings are normally distributed, and if one thermometer is randomly selected, find the probability that, at the freezing point of water the reading is less than 1.58°C. Look in Table A-­2: z .08 1.5 EVERY PROBLEM-­YOU WILL DRAW A PICTURE! Find P( freezing point reads below 1.58 ) Find P(freezing point reads above -­1.23) Find P(freezing point reads between -­2 and 1.52) Notation: P(a < z < b) P(z > a) P(z < a)