Question

(a)
which has the larger standard deviation?
o figure (a)
o figure (b)
what is the mean of the curve in figure (a)?
what is the mean of the curve in figure (b)?

Explanation:

Step1: Recall the relationship between standard deviation and the shape of the normal curve

A larger standard deviation means the data is more spread out. A flatter normal curve (wider) has a larger standard deviation. Figure (a) is flatter (wider) than figure (b).

Step2: Find the mean of a normal curve

The mean of a normal curve is at the center (the peak) of the curve. For figure (a), the center (peak) is at \(x = 11\). For figure (b), the center (peak) is at \(x=6\).

Answer:

• Which has the larger standard deviation: Figure (a)
• What is the mean of the curve in figure (a): \(11\)
• What is the mean of the curve in figure (b): \(6\)