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?