Question

1What happens to the curve when the standard deviation is increased? What does that do to the area under the curve?


2What happens to the curve when the standard deviation is decreased? What does that do to the area under the curve?

Answer 1

Answer:

The answer is below

Explanation:

Z score is a score used in mathematics to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

$z=\frac{x-\mu}{\sigma}\\\\where\ x=raw\ score, \mu=mean,\sigma=standard\ deviation. \\\\For\ a\ sample\ size(n):\\\\ z=\frac{x-\mu}{\sigma/\sqrt{n} }$

The area under the curve is dependent on the z score. The higher the z score, the higher the area under curve and the lower the z score, the lower the area under curve.

a) The area under curve (z score) is inversely proportional to the standard deviation. If the standard deviation is increased, the z score decreases thereby reducing the area under the curve.

b) If the standard deviation is decreased, the z score increases thereby increasing the area under the curve.