Questions and Answers
What is a normal distribution?
A statistical distribution of data which is symmetrical and in which the mean, median, and mode are equal.
What is a standard normal curve?
A graph of the standard normal distribution.
What is the standard normal distribution?
A normal distribution in which the mean is 0 and the standard deviation is 1.
Match the following terms to their correct descriptions:
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How many batteries can be expected to last between three years and one month and three years and seven months in a production run of 25,000 batteries with a mean shelf life of three years and four months and a standard deviation of three months?
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In the Men's Shot Put qualifying round at the 2012 Summer Olympic Games, what percent of athletes would have had a distance greater than 20.56 meters, one standard deviation above the mean?
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How many people had scores lower than Carlos, who scored 31 on a standardized test with a mean score of 21 and a standard deviation of 5?
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In a bin of 100 large apples, how many can be expected to have a diameter greater than 11.5 cm, if the mean diameter is 10 cm with a standard deviation of 0.5 cm?
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Find f(g(x)) given f(x)=2x-5 and g(x)=5x+3.
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What is the standard form for the equation of the ellipse given by 5x^2+4y^2-20x-24y=-36?
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Find the roots of the equation (3x-1)(2x+5)=0.
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Study Notes
Normal Distribution
- A statistical distribution characterized by symmetry, where the mean, median, and mode are equal.
Standard Normal Distribution
- A specific case of normal distribution with a mean of 0 and a standard deviation of 1.
Standard Normal Curve
- The graphical representation of the standard normal distribution.
Application of Normal Distribution
- Example: A flashlight battery's mean shelf life is 3 years and 4 months, with a standard deviation of 3 months. Out of 25,000 batteries, approximately 17,050 are expected to last between 3 years and 1 month and 3 years and 7 months.
Percentiles and Athletes' Performance
- At the 2012 Summer Olympics, the mean shot put distance was 19.64 meters with a standard deviation of 0.92 meters. About 6 out of 40 athletes would exceed 20.56 meters, one standard deviation above the mean.
Standardized Test Scoring
- For a test with a mean score of 21 and standard deviation of 5, Carlos scored 31, which is two standard deviations above the mean. Out of 1.5 million test takers, approximately 1,465,500 scored lower than Carlos.
Characteristics of Apple Sizes
- Large apples at a grocery store have a mean diameter of 10 cm and standard deviation of 0.5 cm. No apples are expected to exceed 11.5 cm, which is three standard deviations above the mean.
Functions Composition
- For functions ( f(x) = 2x - 5 ) and ( g(x) = 5x + 3 ), the composition results in ( f(g(x)) = 10x + 1 ).
Ellipse Equation Standard Form
- The standard form of the ellipse equation derived from ( 5x^2 + 4y^2 - 20x - 24y = -36 ) is ( \frac{(x-2)^2}{4} + \frac{(y-3)^2}{5} = 1 ).
Finding Roots of an Equation
- The roots of the equation ( (3x-1)(2x+5) = 0 ) are ( -\frac{5}{2} ) and ( \frac{1}{3} ).
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Test your knowledge on normal distributions with these flashcards. Each card presents key terms and definitions related to statistics, particularly focusing on normal and standard distributions. Perfect for Algebra 2 students looking to solidify their understanding of these concepts.
