Questions: Find the indicated area under the standard normal curve. To the left of z=-1.78 Click here to view page 1 of the standard normal table. The area to the left of z=-1.78 under the standard normal curve is (Round to four decimal places as needed.)

Solution Steps

We need to find the area under the standard normal curve to the left of $z = -1.78$. This area can be represented mathematically as $P(Z < -1.78)$.

The area to the left of a given $z$-score can be calculated using the cumulative distribution function (CDF) of the standard normal distribution, denoted as $\Phi(z)$. Therefore, we can express the area as: $$P(Z < -1.78) = \Phi(-1.78) - \Phi(-\infty)$$ Since $\Phi(-\infty) = 0$, this simplifies to: $$P(Z < -1.78) = \Phi(-1.78)$$

From the calculations, we find that: $$\Phi(-1.78) = 0.0375$$ Thus, the area to the left of $z = -1.78$ under the standard normal curve is $0.0375$.

Final Answer