In the image, the problem asks to choose the correct graph that represents the scenario. Here is a detailed breakdown:

The problem appears to be about the normal distribution of the time to complete a test. It mentions:

• The time to complete the test is normally distributed.
• The mean time is 10 minutes.
• The standard deviation is 1 minute.
• The goal is to determine the probability of a randomly selected subject completing the test in less than 9 minutes.

Key points:

1. The normal distribution is centered at the mean (10 minutes).
2. You're asked to find the probability of a test being completed in less than 9 minutes, which corresponds to the area under the curve to the left of 9 on a normal distribution curve.

How to Solve:

• Since the mean is 10 and the standard deviation is 1, the point 9 minutes is exactly 1 standard deviation below the mean.
• The area under the curve to the left of 9 minutes represents the cumulative probability.

Correct Graph:

Look for the graph that shows:

• A shaded area to the left of 9 minutes.
• The curve should be centered at 10 minutes (the mean), and 9 minutes should be 1 standard deviation away to the left.

The correct graph will have shading starting from the leftmost side of the graph and extending to the point labeled 9 minutes.

Based on the image, the correct answer appears to be graph B, as it is the one with the shaded region to the left of 9 minutes.

Would you like further explanation on how to calculate the area under the normal curve or any additional details on normal distributions?

Relative Questions:

1. How is the cumulative probability in a normal distribution calculated?
2. What is the empirical rule for standard deviations in a normal distribution?
3. What is the significance of z-scores in normal distribution problems?
4. How do you compute the probability for values greater than a given point in a normal distribution?
5. How can we use the standard normal table to find probabilities?

Tip:

When solving normal distribution problems, always visualize the mean and standard deviation on the curve to better understand the shaded areas representing probabilities.