1. **State the problem:** We want to find the probability that a pig weighs less than 162 lbs given the mean weight $\mu = 167$ lbs and standard deviation $\sigma = 4$ lbs. 2. **Formula and explanation:** We use the standard normal distribution to find this probability. The formula to convert a value $x$ to a $z$-score is: $$z = \frac{x - \mu}{\sigma}$$ This $z$-score tells us how many standard deviations $x$ is from the mean. 3. **Calculate the $z$-score:** $$z = \frac{162 - 167}{4} = \frac{-5}{4} = -1.25$$ 4. **Find the probability:** We look up the value of $z = -1.25$ in the standard normal distribution table. The table gives the probability that $Z$ is less than $-1.25$. From the table, $P(Z < -1.25) = 0.10565$. 5. **Interpretation:** The probability that a pig weighs less than 162 lbs is approximately $0.10565$. **Final answer:** $$P(X < 162) = 0.10565$$