Normal Probability Distributions Chapter 5. § 5.3 Normal Distributions: Finding Values.

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Presentation transcript:

Normal Probability Distributions Chapter 5

§ 5.3 Normal Distributions: Finding Values

Larson & Farber, Elementary Statistics: Picturing the World, 3e 3 Finding z-Scores Example : Find the z - score that corresponds to a cumulative area of z Find the z - score by locating in the body of the Standard Normal Table. The values at the beginning of the corresponding row and at the top of the column give the z - score. The z - score is Appendix B: Standard Normal Table

Larson & Farber, Elementary Statistics: Picturing the World, 3e 4 Finding z-Scores Example : Find the z - score that corresponds to a cumulative area of z   Find the z - score by locating in the body of the Standard Normal Table. Use the value closest to     Appendix B: Standard Normal Table Use the closest area. The z - score is  

Larson & Farber, Elementary Statistics: Picturing the World, 3e 5 Finding a z-Score Given a Percentile Example : Find the z - score that corresponds to P 75. The z - score that corresponds to P 75 is the same z - score that corresponds to an area of The z - score is ?μ =0 z 0.67 Area = 0.75

Larson & Farber, Elementary Statistics: Picturing the World, 3e 6 Transforming a z-Score to an x-Score To transform a standard z - score to a data value, x, in a given population, use the formula Example : The monthly electric bills in a city are normally distributed with a mean of $120 and a standard deviation of $16. Find the x - value corresponding to a z - score of We can conclude that an electric bill of $ is 1.6 standard deviations above the mean.

Larson & Farber, Elementary Statistics: Picturing the World, 3e 7 Finding a Specific Data Value Example : The weights of bags of chips for a vending machine are normally distributed with a mean of 1.25 ounces and a standard deviation of 0.1 ounce. Bags that have weights in the lower 8% are too light and will not work in the machine. What is the least a bag of chips can weigh and still work in the machine? The least a bag can weigh and still work in the machine is 1.11 ounces. ? 0 z 8% P(z < ?) = 0.08 P(z <  1.41) = 0.08  x ? 1.11