1. The problem asks for the probability that a normally distributed random variable $C$ with mean $\mu=22$ and standard deviation $\sigma=8$ is less than 20, i.e., $P(C < 20)$.\n\n2. We use the standard normal distribution to find this probability by converting $C$ to the standard normal variable $Z$ using the formula: $$Z = \frac{C - \mu}{\sigma}$$\n\n3. Calculate the $Z$-score for $C=20$: $$Z = \frac{20 - 22}{8} = \frac{-2}{8} = -0.25$$\n\n4. Now, find $P(Z < -0.25)$ using the standard normal distribution table or a calculator. The value is approximately 0.4013.\n\n5. Therefore, $P(C < 20) = 0.4013$.