# Normal Distribution Calculator

Author:
Rachel
Seeing data in the Normal Distribution Curve Use the Normal Distribution Calculator to complete these problems. 1. Fill in the blanks for the following properties of normal distributions: a) The MEAN is located on the ___ of the Normal Curve. b) In the PROBABILITY of: column, click on the BETWEEN box and change the values in the boxes that appear to -3 ≤ x ≤ 3. What is the probability ____? c) Now change the values in these BETWEEN boxes to -1 ≤ x ≤ 1. What is the probability ____? d) Now change the values in these BETWEEN boxes to 1 ≤ x ≤ 3. What is the probability ____? 2. Fill in the blanks for the following properties of normal distributions: a) About ___% of the area under the curve is within 1 standard deviation to the left of the mean. Change the numbers in the PROBABILITY of: BETWEEN boxes to -1 ≤ x ≤ 0. b) About __% of the area under the curve is 2 and 3 standard deviations to the right of the mean. Change the numbers in the PROBABILITY of: BETWEEN boxes to 1 ≤ x ≤ 2. c) About ___% of the area under the curve is within1 standard deviations from the mean. Change the numbers in the PROBABILITY of: BETWEEN boxes to -3 ≤ x ≤ -2. d) How do you know the above values are true? (not because the calculator said so) What is it about the Normal Curve that allows you to be certain? 3. A set of 360 data points are normally distributed with a mean of 180 and a standard deviation of 45. a) What is the probability that a value will be between 90 and 270? What information on the curve was used to find this probability? b) What is the probability that a value will be below 180? Why is this true? c) What is the mean of this data?