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Z-Scores and The Standard Normal Distribution
Midterm Review Z-Scores and The Standard Normal Distribution
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1st and 2nd Exams Next Week - Midterm Exam Schedule Morning Afternoon
Monday Regular B Day Schedule β Review Day Tuesday 1st and 2nd Exams 3rd and 4th REVIEW Wednesday 5th and 6th Exams 7th and 8th REVIEW Thursday 3rd and 4th Exams No Classes Friday 7th and 8th Exams
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Resources for Studying
Unit Tests and Quizzes Notes Classwork, Problem Sets, and Homeworks YouTube
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π=π π=1
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For All Normal Distributions
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Soβ¦ for the first three standard deviations from the mean we know how to find the percentage of data included! If we want to know the percentage of the population above, below, or between any values β¦ we can use the z-score! The z-score tells us the number of standard deviations between any value and the mean of the population.Β
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Standard Deviation of population
Mean of population value π§= π₯βπ π z-score Standard Deviation of population
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Example C What is theΒ z-score of a value of 27, given a set mean of 24, and a standard deviation of 2? π= πβπ π π= (ππ)β(ππ) (π) π= π π π=π.π
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Example D What is the z-score of a value of 104.5, in a set with π=125 and π=6.2? π= πβπ π π= (πππ.π)β(πππ) (π.π) π= βππ.π π.π π=βπ.ππ
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Quick Practice 4. What is theΒ z-score of the price of a pair of skis that cost $247, if the mean ski price is $279, with a standard deviation of $16? 5. What is theΒ z-score of a 5-scoop ice cream cone if the mean number of scoops is 3, with a standard deviation of 1 scoop? 6. What is theΒ z-score of the weight of a cow that tips the scales at 825 lbs, if the mean weight for cows of her type is 1150 lbs, with a standard deviation of 77 lbs?
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Tips for reading Z-Score Tables
Z-score tables give us the probability that a value or any value less than it, will occur. Always start by converting to a % β¦. (multiply by 100%) To find the percentage of valuesΒ greaterΒ than aΒ z-score, subtract this % from 100%.
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ππ.ππ% What is the probability of a z-score less than 0.54? ____________ What is the probability of a z-score greater than 0.54? ____________ What is the probability of a z-score less than -0.93? ____________ What is the probability of a z-score greater than -0.93? ____________ What is the probability of a z-score greater than 0.81? ____________ What is the probability of a z-score less than -0.81? ____________ ππ.ππ% ππ.ππ% ππ.ππ% ππ.ππ% ππ.ππ%
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Examples E. What is the probability that a value with a z-score less than 2.47 will occur in a normal distribution? F. What is the probability that a value with a z-score greater than 1.53 will occur in a normal distribution? G. What is the probability of a random selection being less than 3.65, given a normal distribution with π=5 πππ π=2.2?
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