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60, 70, 78, 88, 88, 88, 93, 96 ________ Med = ___________ Mode = _________ Range = _________ __________ Warm-up

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7.4 Normal Distributions

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Z - Scores

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EXAMPLE 3 Use a z-score and the standard normal table Scientists conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed during each survey. The numbers of seals observed were normally distributed with a mean of 73 seals and a standard deviation of 14.1 seals. Find the probability that at most 50 seals were observed during a survey. Biology P(x < 50) = P(z < – 1.6) =

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EXAMPLE 3 Use a z-score and the standard normal table Page 296

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GUIDED PRACTICE for Example 3 8. WHAT IF? In Example 3, find the probability that at most 90 seals were observed during a survey. 0.8849 ANSWER

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GUIDED PRACTICE for Example 3 9. REASONING: Explain why it makes sense that P(z < 0) = 0.5. A z- score of 0 indicates that the z- score and the mean are the same. Therefore, the area under the normal curve is divided into two equal parts with the mean and the z- score being equal to 0.5. ANSWER

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Daily Homework Quiz For use after Lesson 11.3 0.025 ANSWER 1. A normal distribution has mean x and standard deviation. For a randomly selected x -value from the distribution, find P(x x – 2 ).

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2. The average donation during a fund drive was $75. The donations were normally distributed with a standard deviation of $15. Use a standard normal table to find the probability that a donation is at least $115. ANSWER 0.35 % or 0.0035

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Warm Up 1.What is the distance between the points (2, -5) and (-4, 7)? 2. Determine the center and radius for the circle with (-5, 2) and (3, -2) as endpoints.

Warm Up 1.What is the distance between the points (2, -5) and (-4, 7)? 2. Determine the center and radius for the circle with (-5, 2) and (3, -2) as endpoints.

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