Area Left Z
1. The problem asks for the area under the standard normal curve to the left of $z = -1.42$.
2. The standard normal distribution is a normal distribution with mean $\mu = 0$ and standard deviation $\sigma = 1$.
3. The area to the left of a $z$-score corresponds to the cumulative probability $P(Z \leq z)$.
4. To find this area, we use the standard normal cumulative distribution function (CDF), often found in $z$-tables or calculated using software.
5. Looking up $z = -1.42$ in the standard normal table or using a calculator, we find:
$$P(Z \leq -1.42) \approx 0.0778$$
6. This means approximately 7.78% of the data lies to the left of $z = -1.42$ under the standard normal curve.
Final answer: The area under the normal curve to the left of $z = -1.42$ is approximately $0.0778$.