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Area Left Z

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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 $0.0778$.