24AB NORMAL DISTRIBUTIONS & PROBABILITIES WITH A CALCULATOR.

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Presentation transcript:

24AB NORMAL DISTRIBUTIONS & PROBABILITIES WITH A CALCULATOR

VIDEO on/intro.mp4 on/intro.mp4 Goodie

BASED ON THE VIDEO, 1. Which are other names for the normal distribution? Select all that apply. A.Typical curve B.Gaussian curve C.Regular distribution D.Galileo curve E.Bell-shaped curve F.Laplace's distribution

BASED ON THE VIDEO, 2. Select all of the statements that are true about normal distributions. A.They are symmetric around their mean. B.The mean, median, and mode are equal. C.They are defined by their mean and skew. D.The area under the normal curve is equal to 1.0. E.They have high density in their tails.

NORMAL DISTRIBUTION The normal distribution is the most important and most widely used distribution in statistics. Examples of data that are normally distributed: heights & weights of people, Scores for tests taken by a large amount of people (ex. SAT) dimensions of manufactured goods

CHARACTERISTICS OF A NORMAL DISTRIBUTION Normal distributions are symmetric around their mean. The mean, median, and mode of a normal distribution are equal. The area under the normal curve is equal to 1.0. Normal distributions are denser in the center and less dense in the tails. Normal distributions are defined by two parameters, the mean (μ) and the standard deviation (σ).

PROBABILITY DENSITY FUNCTION

NOTATION A random variable is a function that associates a unique numerical value with every outcome of an experiment.

EXAMPLE The chest measurements of 18 year old male footballers are normally distributed with a mean of 95 cm and a standard deviation of 8 cm. Represent this information on a normal curve. What percent of the data is between 87 and 103 cm? What percent of the data is greater than 111 cm? 68.3% 2.28%

EXAMPLE The chest measurements of 18 year old male footballers are normally distributed with a mean of 95 cm and a standard deviation of 8 cm. Find the percentage of footballers with chest measurements between: 87 cm and 103 cm 103 cm and 111 cm Find the probability that the chest measurement of a randomly chosen footballer is between 87 cm and 111 cm. Find the value of k such that approximately 16% of chest measurements are below k. 68.3% 13.6% k = 87 cm

FURTHER EXPLANATION OF LAST QUESTION Find the value of k such that approximately 16% of chest measurements are below k.

The area under a normal curve represents the proportion of data at (or between) data values. The total area under a normal curve is 1. (100%) Shaded area = proportion of data less than x = percent of data less than x AREA UNDER THE NORMAL CURVE

NOTATION The notation below states: “The probability that the random variable is less than or equal to a.” “The probability that the random variable is greater than or equal to a and less than or equal to b.” A random variable is a function that associates a unique numerical value with every outcome of an experiment.

24B: PROBABILITIES WITH A CALCULATOR

EXAMPLE TIME!

ANOTHER AWESOME EXAMPLE:

INVNORM HELP InvNorm calculator help:

HOMEWORK – YIPEE! 24A: Your choice of 5 problems from #1 – B: Your choice of 4 problems from #1 – 8.