12.3 Normal Distributions

1. Draw and label a normal distribution with the given parameters:

For each of the following questions, draw and label a normal curve that represents the question asked. 2. Human IQ tests are frequently adjusted to a normal distribution where ! = 100; and' = 16. a. What proportion of scores would be at least a 70? b. What proportion of scores would be below a 120? c. What proportion of scores would be between 90 and 110? d. What score would be at the 50th percentile? At the 10th percentile? 3. Bernadette loves coffee! And it makes her late most of the time. On average, the number of minutes Bernadette is late can be described by a normal distribution with parameters ! = 35; and' = 20 minutes. a. On average, how many minutes late is Bernadette to work? b. What percent of the time does Bernadette come between 0 and 50 minutes late? c. What percent of the time does Bernadette come more than an hour late? d. If Bernadette comes to work 190 days, about how many will she be on time? e. What score represents the 2nd percentile? Explain what this score means.

a. ! = 10; ' = 2

b. ! = 10; ' = 3

c. ! = 30; ' = 1

d. ! = 0.5; ' = 0.2

e. ! = 100; ' = 15

f. ! = 0; ' = 1

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4. Suppose PSAT scores for 11th graders are normally distributed with ! = 969; and' = 168. a. What was an average score for an 11th grader? b. What score would be considered at the 80th percentile? c. What percent of scores are between 600 and 1100? d. If a school has about 200 11th graders, about how many will score above 1200? e. What was your latest score on the PSAT? Use your score to find your percentile on the PSAT.

5. Solve for x: 5/0 + / = 4 6. Describe the end behavior of 3(/) = 4/6 − 2/0 − 12 7. Find the exact value of tan(135°) ? 8. Is (/ − 2) a factor of =(/) = 3/0 + / − 14 ?

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