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Bennie Waller wallerbd@longwood 434-395-2046

Bennie Waller wallerbd@longwood.edu 434-395-2046 Longwood University 201 High Street Farmville, VA 23901. Bennie Waller wallerbd@longwood.edu 434-395-2046 Longwood University 201 High Street Farmville, VA 23901. Continuous Distributions.

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Bennie Waller wallerbd@longwood 434-395-2046

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  1. Bennie Waller wallerbd@longwood.edu 434-395-2046 Longwood University201 High StreetFarmville, VA 23901

  2. Bennie Waller wallerbd@longwood.edu 434-395-2046 Longwood University201 High StreetFarmville, VA 23901

  3. Continuous Distributions Characteristics of a Normal Probability Distribution • It is bell-shaped. • It is symmetricalabout the mean • It is asymptotic: • The location of a normal distribution is determined by the mean,, the dispersion is determined by the standard deviation,σ . • The arithmetic mean, median, and mode are equal • The total area under the curve is 1.00; half the area under the normal curve is to the right of this center point, the mean, and the other half to the left of it. 7-3

  4. Equal Means and Different Standard Deviations

  5. The Standard Normal Probability Distribution • The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. • It is also called the z distribution. • A z-value is the signed distance between a selected value, designated X, and the population mean , divided by the population standard deviation, σ. • The formula is: 7-8

  6. Areas Under the Normal Curve

  7. Problem: The weight of a bag of corn chips is normally distributed with a mean of 22 ounces and a standard deviation of ½ ounces. What is the probability that a bag of corn chips weighs more than 23 ounces?  

  8. Problem: A sample of 500 evening students revealed that their annual incomes were normally distributed with a mean income of $30,000 and a standard deviation of $3,000. How many students earned between $27,000 and $33,000?

  9. Problem: The weight of a bag of corn chips is normally distributed with a mean of 22 ounces and a standard deviation of ½ ounces. What is the probability that a bag of corn chips weighs between 20.75 and 23.25 ounces?  

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