1. Use the normal table to find the area under the curve for each of the following z-scores:
(a) $z < -2.25$
(b) $z > .54$
(c) $-2.25 < z < .54$
2. Acid Rain: Based on long-term investigation, researchers have suggested that the acidity (pH) of
rainfall in Shenandoah Mountains can be described by the Normal model $N(4.9, 0.6)$ (the notation
implies that we have a normal distribution with a mean, $\mu$, of 4.9 and a standard deviation, $\sigma$, of
0.6)
(a) What percent of storms produce rain with a pH less than 4?
(b) What percent of storms produce rainfall between 4 and 6?
3. You have a population distributed in an unknown way. However, you do know
that the mean = 20 and the standard deviation = 12. Take a sample of size 45.
a) What is the mean of this distribution?
b) The standard deviation?
c) Find the probability the sample mean is less than 23.
