\( 1 \leftarrow \begin{array}{l}\text { Find the indicated probability using the standard normal distribution. } \\ \qquad(z<-2.28) \\ \frac{\text { Click here to view page } 1 \text { of the standard normal table. }}{\text { Click here to view page } 2 \text { of the standard normal table. }} \\ P(z<-2.28)=\square \text { (Round to four decimal places as needed.). }\end{array} \).

To find the probability \( P(z < -2.28) \) using the standard normal distribution, you can refer to the standard normal table (z-table) which provides the area to the left of a given z-value. Looking up \( z = -2.28 \), you’ll find that the corresponding probability is approximately 0.0116. This means that about 1.16% of the data lies below this z-score in a standard normal distribution. For real-world applications, understanding the concept of z-scores is essential in fields like psychology, finance, and quality control. For instance, in quality control, a z-score can help determine if a batch of products meets acceptable quality standards, allowing businesses to make informed decisions based on statistical analysis. So, next time you see a z-score, think of the powerful insights it can provide!