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CCHS Chapter 5 Sections 5.1 & 5.2 Practice Name__________________________________________________ Date__________ Period_______ For 1 & 2, draw a normal curve and fill in the values for the mean and 1, 2, and 3 standard deviations; 1. A Dogs Life Span The life span of a dog is normally distributed with a mean of 12.5 years and a standard deviation of 2 years. Estimate the probability that a dog’s life span is between 10.5 and 14.5 years. 2. Light Bulb Life Span The life span of a certain type of light bulb is normally distributed with a mean of 5000 hours and a standard deviation of 150 hours. Estimate the probability that this type of light bulb has a life span is between 4850 and 5300 hours. Finding Area in Exercises 3-8, find the indicated area under the standard normal curve. (Hint: Draw a picture) 3. Between z = 0 and 1.28 4. Between z = 0 and z = -2.12 5. To the right of z = 2.40 6. To the left of z = -0.46 7. Between z = 1.23 and z = 1.90 8. Between z = -1.45 and z = 1.87 Finding Probabilities In Exercises 9-14, find the probabilities for each using the standard normal distribution. 9. P (-1.25< z < 0) 12. P (z > -0.5) 10. P (z > 2.53) 13. P (-2.05 < z < 1.85) 11. P (z < -1.25) 14. P (z < -1.54 or z > 1.54) Mambou 1:42:42 PM 6/24/2017 CCHS 15. What is the total area underneath the normal curve? 16. What percentage of the area falls above the mean? True or False. 17. The area under the curve for a normal distribution is 1. T or F 18. The mean, mode and media are all equal for a normal distribution. T or F 19. The area under the standard normal curve that lies within two standard deviations from the mean is approximately 95%. T or F 20. A distribution is said to be positively skewed if the mean falls to the right of the mean. T or F Graphical Analysis In Exercises 21-26, find the probability of z occurring in the indicated region. 21. 22. 23. 24. 26. Bags of Flour The weights of bags of flour are normally distributed, with a mean of 5 pounds (80 ounces) and a standard deviation of 0.5 ounce. Determine an interval of values into which (a) about 95% of the bags of flour will fall and (b) about 68% of the bags of flour will fall. Mambou 1:42:42 PM 6/24/2017 CCHS Chapter 6 Sections 5.1 & 5.2Practice Name___________________Keys_____________________ Date__June 24, 2017_ Period_______ For 1 & 2, draw a normal curve and fill in the values for the mean and 1, 2, and 3 standard deviations; 1. A Dogs Life Span The life span of a dog is normally distributed with a mean of 12.5 years and a standard deviation of 2 years. Estimate the probability that a dog’s life span is between 10.5 and 14.5 years. Within one standard deviation from the mean the probability is about 68% 2. Light Bulb Life Span The life span of a certain type of light bulb is normally distributed with a mean of 5000 hours and a standard deviation of 150 hours. Estimate the probability that this type of light bulb has a life span is between 4850 and 5300 hours. 0ne standard deviation to the left or 34% and two standard deviation to the right 47.5% the sum is 81.5 % Finding Area in Exercises 3-8, find the indicated area under the standard normal curve. (Hint: Draw a picture) 3. Between z = 0 and 1.28 Normalcdf (0, 1.28) 0.3997 4. Between z = 0 and z = -2.12 Normalcdf (-2.12, 0) 0.4830 5. To the right of z = 2.40 Normalcdf (2.40, 10) 0.0082 6. To the left of z = -0.46 Normalcdf (-0.46, 10) 0.6772 7. Between z = 1.23 and z = 1.90 Normalcdf (1.23, 1.90) 0.0806 8. Between z = -1.45 and z = 1.87 Normalcdf (-1.47, 1.87) 0.8985 Finding Probabilities In Exercises 9-14, find the probabilities for each using the standard normal distribution. 9. P(-1.25< z < 0) Normalcdf(-1.25, 0) 0.3944 12. P(z > -0.5) Normalcdf -0.5, 10) 0.6915 10. P(z > 2.53) 13. P(-2.05 < z < 1.85) Normalcdf (2.53, 10) Normalcdf (-2.05, 1.85) 0.0057 0.9477 11. P(z < -1.25) 14. P(z < -1.54 or z > 1.54) Normalcdf (-10, -1.25) Normalcdf (-10,-1.54) + Normalcdf (1.54,10) 0.1056 0.1236 15. What is the total area underneath the normal curve? 1 or 100% 16. What percentage of the area falls above the mean? 50% True or False. Mambou 1:42:42 PM 6/24/2017 CCHS 17. The area under the curve for a normal distribution is 1. T or F 18. The mean, mode and media are all equal for a normal distribution. T or F 19. The area under the standard normal curve that lies within two standard deviations from the mean is approximately 95%. T or F 20. A distribution is said to be positively skewed if the mean falls to the right of the mean. T or F Graphical Analysis In Exercises 21-26, find the probability of z occurring in the indicated region. 21. Normalcdf (0, 2.25) 0.4878 23. Normalcdf (-10, 1.27) 0.8980 22. 2* Normalcdf (1.29, 10) 0.0985 24. Normalcdf (-0.87, 10) 0.8078 26. Bags of Flour The weights of bags of flour are normally distributed, with a mean of 5 pounds (80 ounces) and a standard deviation of 0.5 ounce. Determine an interval of values into which (a) about 95% of the bags of flour will fall and (b) about 68% of the bags of flour will fall. a/ 95% 80 – 2*0.5 = 79 ounces 80+2*0.5 = 81 ounces within 79 and 81 ounces b/79.5 and 80.5 ounces for 68% Mambou 1:42:42 PM 6/24/2017