$$ =1=2 $$ Use the 3 Cumulative Normal Distribution Table to find the $$ z $$-score for which the area to its left is 0.09 . The $$ z $$-score for the given area is $$ \square $$.

Question

UpStudy AI · Accepted Answer

To find the $$ z $$-score for which the area to its left is 0.09 using the standard normal distribution table (often referred to as the Z-table), follow these steps:

### Step 1: Understand the Problem

You're looking for the $$ z $$-score ($$ z $$) such that:
$$ P(Z \leq z) = 0.09 $$

This means that 9% of the distribution lies to the left of $$ z $$.

### Step 2: Locate the Area in the Z-Table

1. **Symmetry Consideration:**
   - Since 0.09 is less than 0.5, $$ z $$ will be **negative** because the mean of the standard normal distribution is 0.
   
2. **Using the Z-Table:**
   - Z-tables typically provide the area to the **left** of a positive $$ z $$-score.
   - To find a negative $$ z $$-score corresponding to an area of 0.09, find the positive $$ z $$-score that leaves 0.09 in the left tail.

### Step 3: Find the Corresponding $$ z $$-Score

1. **Look Up 0.09 in the Table:**
   - You need to find the $$ z $$-score where the cumulative area is closest to 0.09.
   
2. **Approximation:**
   - Upon checking the Z-table, you'll find that:
     $$ P(Z \leq -1.34) \approx 0.0901 $$
   
   - This is very close to the desired area of 0.09.

### Step 4: Conclusion

The $$ z $$-score corresponding to an area of 0.09 to its left is approximately:

$$
\boxed{-1.34}
$$
The $$ z $$-score for an area of 0.09 to its left is approximately **-1.34**.

Use the 3 Cumulative Normal Distribution Table to find the -score for which the area to its left is 0.09 .
The -score for the given area is .

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Statistics Questions

Use the 3 Cumulative Normal Distribution Table to find the -score for which the area to its left is 0.09 . The -score for the given area is .