Find the indicated probability using the standard normal distribution. $$ P(-1.86

Question

UpStudy AI · Accepted Answer

To find the probability $$ P(-1.86 < z < 0) $$ using the standard normal distribution, we can break it down into two parts:

1. Find $$ P(z < 0) $$
2. Find $$ P(z < -1.86) $$
3. Subtract the second probability from the first to get $$ P(-1.86 < z < 0) $$.

### Step 1: Find $$ P(z < 0) $$

The standard normal distribution is symmetric around zero. Therefore, the probability that $$ z $$ is less than 0 is:

$$
P(z < 0) = 0.5
$$

### Step 2: Find $$ P(z < -1.86) $$

Next, we need to look up the value of $$ P(z < -1.86) $$ in the standard normal table.

From the standard normal table, we find:

$$
P(z < -1.86) \approx 0.0314
$$

### Step 3: Calculate $$ P(-1.86 < z < 0) $$

Now we can calculate the probability:

$$
P(-1.86 < z < 0) = P(z < 0) - P(z < -1.86)
$$

Substituting the values we found:

$$
P(-1.86 < z < 0) = 0.5 - 0.0314 = 0.4686
$$

### Final Answer

Thus, the probability $$ P(-1.86 < z < 0) $$ rounded to four decimal places is:

$$
\boxed{0.4686}
$$
The probability $$ P(-1.86 < z < 0) $$ is 0.4686.

Find the indicated probability using the standard normal distribution. \( P(-1.86

Ask by Elliott Fuentes. in the United States

Feb 03,2025