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Find a z-score given the area under the normal curve Transform a z-score to an x-value Find a specific data value of a normal distribution given the probability.

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Presentation on theme: "Find a z-score given the area under the normal curve Transform a z-score to an x-value Find a specific data value of a normal distribution given the probability."— Presentation transcript:

1 Find a z-score given the area under the normal curve Transform a z-score to an x-value Find a specific data value of a normal distribution given the probability

2  Finding a z-Score Given an Area 1. Find the z-score that has 96.16% of the distribution’s area to the right. 2. Find the z-score for which 95% of the distributions area lies between –z and z and 1.96

3  Finding a z-Score Given a Percentile Find the z-score that corresponds to each percentile. 1. P₁₀ 2. P₂₀ 3. P₉₉

4 To transform a standard z- score to a data value x in a given population, use the formula x = µ+zα

5  Finding an x-Value Corresponding to a z-Score A veterinarian records the weights of dogs treated at a clinic. The weights are normally distributed, with a mean of 52 pounds and a standard deviation of 15 pounds. Find the weights x corresponding to z-scores of -2.33, 3.10, and Interpret your results , 98.5, and 60.7

6  Finding a Specific Data Value The braking distances of a sample of Nissan Altimas are normally distributed, with a mean of 129 feet and a standard deviation of 5.18 feet. What is the longest braking distance one of these Nissan Altimas could have and still be in the bottom 1%? feet

7  Finding a Specific Data Value The lengths of time employees have worked at a corporation are normally distributed, with a mean of 11.2 years and a standard deviation of 2.1 years. In a company cutback, the lowest 10% in seniority are laid off. What is the maximum length of time an employee could have worked and still be laid off? years


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