Lesson 3 Assignment
1. Two normally distributed sets of data are described below:
[3]
- Data Set A: mean of 15 and a standard deviation of 5
- Data Set B: mean of 15 and a standard deviation of 1
a. Sketch the normal curve for each set of data including a scale on the horizontal
b. Discuss the effects of the mean and standard deviation on the way each graph looks

Step 1 ：Given two normally distributed sets of data, Data Set A and Data Set B. Data Set A has a mean of 15 and a standard deviation of 5. Data Set B also has a mean of 15 but a standard deviation of 1.

Step 2 ：Sketch the normal curve for each set of data. The mean determines the center of the distribution, while the standard deviation determines the spread of the distribution.

Step 3 ：For Data Set A, the curve is centered at the mean of 15 and has a wider spread due to its larger standard deviation of 5.

Step 4 ：For Data Set B, the curve is also centered at the mean of 15 but has a narrower spread due to its smaller standard deviation of 1.

Step 5 ：From the sketches, it can be observed that both curves are centered at the same point since they have the same mean. However, Data Set A has a wider spread due to its larger standard deviation, while Data Set B has a narrower spread due to its smaller standard deviation.

Step 6 ：\(\boxed{\text{Final Answer: The mean determines the center of the distribution, while the standard deviation determines the spread of the distribution. A larger standard deviation results in a wider spread, and a smaller standard deviation results in a narrower spread.}}\)