Bennie D Waller, Longwood University Statistics Bennie Waller 434-395-2046 Longwood University 201 High Street Farmville, VA 23901.

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Bennie D Waller, Longwood University Statistics Bennie Waller Longwood University 201 High Street Farmville, VA 23901

Bennie D Waller, Longwood University Continuous Probability Bennie Waller Longwood University 201 High Street Farmville, VA 23901

Bennie D Waller, Longwood University Characteristics of a Normal Probability Distribution 1.It is bell-shaped. 2.It is symmetrical about the mean 3.It is asymptotic: 4.The location of a normal distribution is determined by the mean, , the dispersion is determined by the standard deviation,σ. 5.The arithmetic mean, median, and mode are equal 6.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 Continuous Distributions

Bennie D Waller, Longwood University Continuous Distributions

Bennie D Waller, Longwood University Normal Distribution Equal Means and Different Standard Deviations

Bennie D Waller, Longwood University Converting to Standard Normal Distribution

Bennie D Waller, Longwood University Converting to Standard Normal Distribution

Bennie D Waller, Longwood University 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 Converting to Standard Normal Distribution

Bennie D Waller, Longwood University Standard Normal Distribution Tables z Areas Under the Normal Curve

Bennie D Waller, Longwood University Standard Normal Distribution Tables z

Bennie D Waller, Longwood University 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? Tables z

Bennie D Waller, Longwood University 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? Tables z

Bennie D Waller, Longwood University 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 and ounces? Tables z

Bennie D Waller, Longwood University End