1. Let x be a continuous random variable. What is the probability that x assumes a single value, such as a (use numerical value)?
2. The following are the three main characteristics of a normal distribution.
A. The total area under a normal curve equals _____.
B. A normal curve is ___________ about the mean. Consequently, 50% of the total area under a normal distribution curve lies on the left side of the mean, and 50% lies on the right side of the mean.
C. Fill in the blank. The tails of a normal distribution curve extend indefinitely in both directions without touching or crossing the horizontal axis. Although a normal curve never meets the ________ axis, beyond the points represented by µ - 3σ to µ+ 3σ it becomes so close to this axis that the area under the curve beyond these points in both directions is very close to zero.
3. For the standard normal distribution, find the area within one standard deviation of the mean that is, the area between μ - σ and μ + σ. Round to four decimal places.