1 / 7

5.3 Normal Distributions: Finding Values

5.3 Normal Distributions: Finding Values. 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. Try it yourself 1. Finding a z -Score Given an Area

lona
Download Presentation

5.3 Normal Distributions: Finding Values

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 5.3 Normal Distributions: Finding Values 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. Try it yourself 1 • Finding a z-Score Given an Area • Find the z-score that has 96.16% of the distribution’s area to the right. • Find the z-score for which 95% of the distributions area lies between –z and z. -1.77 -1.96 and 1.96

  3. Try it yourself 2 • Finding a z-Score Given a Percentile Find the z-score that corresponds to each percentile. • P₁₀ • P₂₀ • P₉₉ -1.28 -0.84 2.33

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

  5. Try it yourself 3 • 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 0.58. Interpret your results. 17.05, 98.5, and 60.7

  6. Try it yourself 4 • 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%? 116.93 feet

  7. Try it yourself 5 • 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? 8.512 years

More Related