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Applications……

Learn how to find probabilities and values of populations represented with a normal distribution using the z-score formula. Practice problems included.

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Applications……

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  1. Applications……

  2. OBJECTIVE Find probabilities using a normal distribution.

  3. RELEVANCE Find probabilities and values of populations whose data can be represented with a normal distribution.

  4. Application Problems…… • Not all distributions are standard normal. You must use the z-score formula to transform normal to standard normal.

  5. Example…… • The mean # of hours an American worker spends on the computer is 3.1 hours per workday. Assume the st. deviation is 0.5 hours. Find the percentage of workers who spend less than 3.5 hours on the computer each workday.

  6. Mean = 3.1 Value = 3.5 St. Dev = 0.5 Answer: ncdf(-1000,0.8)= 0.7881 or 78.81% Remember “less than 3.5”….

  7. You Try The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month?

  8. The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month?

  9. Example…… • Each month, an American household generates an average of 28 pounds of newspapers for garbage or recycling. Assume the st. dev. is 2 lbs. If a household is selected at random, find the probability of its generating a. Between 27 and 31 pounds per mo. b. More than30.2 pounds per month.

  10. Value = 27 and 31 Mean = 28 St. Dev = 2 Answer: ncdf(-0.5,1.5) = 0.6247 “Between 27 and 31 pounds”……

  11. Value = 30.2 Mean = 28 St. Dev = 2 Answer: ncdf(1.1,1000)= 0.1357 “More Than 30.2……”

  12. You Try The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

  13. The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

  14. You Try A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275.

  15. A bank’s loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 and 275.

  16. Example…… • The average time it takes to respond to an emergency call is 25 minutes. The variable is normally distributed and the st. dev is 4.5 minutes. If 80 calls are randomly selected, how many will respond in less than 15 minutes?

  17. Value = 15 Mean = 25 St. Dev = 4.5 Answer: Find the percentage 1st. ncdf(-1000,-2.22) = 0.0132 This means that 1.32% of the 80 will respond in less than 15 minutes. (80)(.0132) = 1.056 = 1 call

  18. Assignment…… • HW Worksheet

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