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The image contains a question related to probability, specifically concerning a normal distribution. I'll extract the content and provide a solution for each part.

### Extracted Question:

**Question 2:**  
Petroleum amounts in 200 liter drums are normally distributed with a mean of 194 liters and a standard deviation of 5 liters.

1. **(a)** Find the probability that a randomly chosen oil drum has less than 190 liters.  
2. **(b)** Determine the percentage of the oil drums containing between 188 liters and 198 liters.  
3. **(c)** 2000 drums are inspected. Estimate how many drums contain between 188 liters and 198 liters of oil.

Let's solve each part step-by-step.

### Solution:

#### Part (a)

To find the probability that a randomly chosen oil drum has less than 190 liters, we need to calculate the Z-score for 190 liters using the formula:

\[
Z = \frac{X - \mu}{\sigma}
\]

Where:
- \( X = 190 \) liters
- \( \mu = 194 \) liters (mean)
- \( \sigma = 5 \) liters (standard deviation)

Calculating the Z-score:

\[
Z = \frac{190 - 194}{5} = \frac{-4}{5} = -0.8
\]

Now, we need to find the cumulative probability for \( Z = -0.8 \) using the standard normal distribution table or a calculator.

The cumulative probability \( P(Z

Petroleum amounts in 200 liter drums are normally distributed with a mean of 194 liters and a standard deviation of 5 liters. (a) Find the probability that a randomly chosen oil drum has less than 190 liters. (b) Determine the percentage of the oil drums containing between 188 liters and 198 liters. (c) 2000 drums are inspected. Estimate how many drums contain between 188 liters and 198 liters of oil.

Explore a probability problem involving normally distributed petroleum amounts in drums. Learn how to calculate the probability for a drum containing less than 190 liters and determine the percentage of drums containing between 188 and 198 liters. Estimate the number of drums in a sample of 2000 that meet the criteria. Suitable for students in Grades 9-12.

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