Questions: 1. State the mean of the distribution of the biology exam scores. 2. State the standard deviation of the distribution of the biology exam scores.

Solution Steps

The mean of a normal distribution is located at the center of the distribution curve. In the given graph, the mean is the value at the peak of the curve.

From the graph, the peak of the curve is at the score of 78. Therefore, the mean of the distribution is 78.

The standard deviation in a normal distribution is the distance from the mean to the inflection points on either side of the curve. The inflection points are where the curve changes concavity.

From the graph, the inflection points are at scores 70 and 86. The distance from the mean (78) to either inflection point is: \[ 78 - 70 = 8 \] or \[ 86 - 78 = 8 \] Thus, the standard deviation is 8.

Final Answer