AP Statistics: Normal Distribution Practice



Mathematical Design: Normal Distribution Practice Name___________________________

IQ scores are argued to have a distribution of N(100, 15). Use what you know about normal distribution to answer the questions below.

1. Using the 68-95-99.7 Rule, determine what percent of people would fall between the following IQ scores:

o 85 and 115 __________

o 55 and 145 __________

o 55 and 115 __________

o 100 and 145 __________

2. Find the z-scores for the following IQ’s:

o 124 ____________

o 76 ____________

o 130 ____________

3. The Unabomber (Ted Kaczynski) has often been cited as having an IQ of 170. What percent of people have the same or a higher IQ? Explain how you determined this.

4. Forrest Gump was supposed to have an IQ of 75 in the movie. What percent of people have the same or lower IQ? Explain how you determined this.

A common test of cognitive abilities is used to diagnose specific disorders and has a distribution of N(52, 5). Use this information to answer the following:

5. A patient diagnosed with Alzheimer’s takes the test and scores a 45. What is the patient’s percentile rank?

6. Another patient diagnosed with Parkinson’s takes the same test and scores a 54. What percent of patients score above this level?

7. Two children being tested for dyslexia score 58 and 43. What percent of people fall between these two children?

8. A private school uses the cognitive test to place its students. The school uses the following percentiles in order to determine what level of difficulty might suit each individual student. Find the score necessary for each percentile.

• 90th percentile ______________

• 70th percentile ______________

• 50th percentile ______________

• 30th percentile ______________

• 10th percentile ______________

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