MATH 106 Week 7 LEO Discussion Topic Exercises

MATH 106 Week 7 LEO Discussion Topic ExercisesRevised: 25 June 2016NORMAL DISTRIBUTION (Online Statistics Education: A Multimedia Course of Study: Chapter 7,Sections: “Areas of Normal Distribution” ; “Standard Normal” ; “Normal Approximation to Binomial”)AREAS OF NORMAL DISTRIBUTION1. For a normal distribution with mean of 100 and a standard deviation of 12, find the number ofstandard deviations the raw score 76 is from the mean (Give answer as a positive value rounded tonearest hundredth).2. For a normal distribution with mean of 120 and a standard deviation of 15, find the number ofstandard deviations the raw score 144 is from the mean (Give answer as a positive value rounded tonearest hundredth).3. For a normal distribution with mean of 80 and a standard deviation of 8, find the number ofstandard deviations the raw score 67 is from the mean (Give answer as a positive value rounded tonearest hundredth).4. For a normal distribution with mean of 62 and a standard deviation of 6, find the number ofstandard deviations the raw score 47 is from the mean (Give answer as a positive value rounded tonearest hundredth).5. A normal distribution has a mean of 40 and a standard deviation of 5. 68% of the distribution can befound between what two numbers?6. A normal distribution has a mean of 20 and a standard deviation of 3. Approximately 95% of thedistribution can be found between what two numbers?7. A normal distribution has a mean of 5 and a standard deviation of 2. What proportion of thedistribution is above 3? Use either the Area Under Normal Distribution Calculator or Z – table link(round answer to nearest thousandth).8. A normal distribution has a mean of 12 and a standard deviation of 3. What proportion of thedistribution is below 7? Use either the Area Under Normal Distribution Calculator or Z – table link(round answer to nearest thousandth).9. A normal distribution has a mean of 120 and a variance of 100. 35% of the area is below whatnumber? Use either the Inverse Normal Distribution Area Calculator or or Z – table link (roundanswer to nearest thousandth).10. A normal distribution of test scores has a mean of 38 and a standard deviation of 6. Everyone scoringat or above the 80th percentile gets placed in an advanced class. What is the cutoff score to get intothe class? Use either the Inverse Normal Distribution Area Calculator or or Z – table link (roundanswer to nearest thousandth).1MATH 106 Week 7 LEO Discussion Topic ExercisesRevised: 25 June 201611. A normal distribution of test scores has a mean of 38 and a standard deviation of 6. What percent ofthe students scored between 30 and 45? Use either the Area Under Normal Distribution Calculatoror Z – table link (round answer to nearest tenth of a percent).STANDARD NORMAL12. A normal distribution has a mean of 16 and a standard deviation of 6. What is the Z score thatcorresponds with 25?13. A normal distribution has a mean of 100 and a standard deviation of 10. What is the Z score thatcorresponds with 122?14. A normal distribution has a mean of 84 and a standard deviation of 7. What is the Z score thatcorresponds with 95?15. A normal distribution has a mean of 75 and a standard deviation of 15. What is the raw score thatcorresponds with a Z score of 1.6?16. A normal distribution has a mean of 200 and a standard deviation of 25. What is the raw score thatcorresponds with a Z score of – 1.5?17. A normal distribution has a mean of 1200 and a standard deviation of 150. What is the raw scorethat corresponds with a Z score of – 0.5?18. A normal distribution has a mean of 18 and a standard deviation of 5. Use either the Area UnderNormal Distribution Calculator or Z – table link to determine the proportion of the scores (area)below 6.19. Use either the Area Under Normal Distribution Calculator or Z – table link to find the area under thestandard normal curve from Z = 0 to Z = 1.4.20. Use either the Area Under Normal Distribution Calculator or Z – table link to find the area under thestandard normal curve from Z = – 2.5 to Z = 0.21. Use either the Area Under Normal Distribution Calculator or Z – table link to find the area under thestandard normal curve from Z = 0 to Z = 0.67.22. Use either the Area Under Normal Distribution Calculator or Z – table link to find the area under thestandard normal curve from Z = – 1.2 to Z = 0.75.23. Use either the Area Under Normal Distribution Calculator or Z – table link to find the area under thestandard normal curve from Z = 0.3 to Z = 2.6.2MATH 106 Week 7 LEO Discussion Topic ExercisesRevised: 25 June 201624. A normal distribution has a mean of 100 and a standard deviation of 10. What is the Z score thatcorresponds with 122? Use either the Area Under Normal Distribution Calculator or Z – table link tofind the area under the standard normal curve from the mean to raw score 122.25. A normal distribution has a mean of 50 and a standard deviation of 5. Use either the Area UnderNormal Distribution Calculator or Z – table link Use the table found at the link Z – table to find thearea under the standard normal curve between raw score of 39 and raw score 59.26. “Cut-It-Up” brand chain saws have an average service life of 120 months with a standard deviation of15 months. Assuming a normal distribution, find the probability that a “Cut-It-Up” chain saw will lastfor more than 140 months. Compute Z score and use either the Area Under Normal DistributionCalculator or Z – table link to compute the corresponding probability.27. Sales of “Cut-It-Up” brand chain saws average $250,000 per year with a standard deviation of$20,000. Assuming a normal distribution, find the probability that “Cut-It-Up” chain saw annualsales will be more than $300,000. Compute Z score and use either the Area Under NormalDistribution Calculator or Z – table link to compute the corresponding probability.28. The mean time for ice cream to freeze is 210 minutes, with a standard deviation of 15 minutes.Assuming a normal distribution, find the probability that ice cream will take less than 190 minutes tofreeze. Compute Z score and use either the Area Under Normal Distribution Calculator or Z – tablelink to compute the corresponding probability.29. You’re the production manager at world-famous Jack’s Breads. The average length of a loaf of “Jack’sBread” is 11.0 inches, with a standard deviation of 0.5 inches. Assuming a normal distribution, findthe probability that a loaf of bread off the production line will be 11.8 inches or longer. Compute Zscore and use either the Area Under Normal Distribution Calculator or Z – table link to compute thecorresponding probability.30. If 120 measurements of the distance between home and work are randomly chosen from a normaldistribution with mean of 15 and standard deviation of 4, how many raw measurements x would beexpected to fall between (and including) 10 and 19? Use either the Area Under Normal DistributionCalculator or Z – table link to compute the corresponding area under the curve to determine thenumber of measurements.31. The average healing time from a particular inpatient surgical procedure is 200 hours, with a standarddeviation of 20 hours. What percentage of the people having this surgical procedure will heal in 170hours or less? Use either the Area Under Normal Distribution Calculator or Z – table link tocompute the corresponding area under the curve to determine the percentage.3MATH 106 Week 7 LEO Discussion Topic ExercisesRevised: 25 June 2016NORMAL APPROXIMATION TO BINOMIAL32. Suppose you have a normal distribution with a mean of 6 and a standard deviation of 1. What is theprobability of getting a Z score of exactly 1.2? Use either the Area Under Normal DistributionCalculator or Z – table link to compute the corresponding probability – but be careful!!33. You decide to use the normal distribution to approximate the binomial distribution. You want toknow the probability of getting exactly 6 tails out of 10 flips. Find the mean and standard deviationof the normal distribution, then compute Z score and use either the Area Under Normal DistributionCalculator or Z – table link to compute the corresponding probability.34. You decide to use the normal distribution to approximate the binomial distribution. You want toknow the probability of getting from 7 to 13 heads out of 20 flips of a fair, two – sided coin. Find themean and standard deviation of the normal distribution, then compute Z scores and use either theArea Under Normal Distribution Calculator or Z – table link to compute the corresponding areaunder the curve to determine cumulative probability.35. Is a normal distribution with the same mean and standard deviation as a binomial distribution aviable approximation to use if the binomial distribution’s number of trials n = 150 and its probabilityof success p = 0.01? Why or why not?4