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This question involves calculating the area under a normal distribution curve for peanut butter jar prices.

The given information is:
- Mean $ \mu = 3.68 $
- Standard deviation $ \sigma = 0.26 $
- We are asked to find the area for prices greater than $4.25.

### Steps:

1. **Standardize the price**: We convert the price into a z-score using the formula:
   \[
   z = \frac{x - \mu}{\sigma}
   \]
   where $ x = 4.25 $, $ \mu = 3.68 $, and $ \sigma = 0.26 $.

2. **Find the area under the normal curve**: Once the z-score is calculated, we can use a standard normal table or a calculator to find the probability corresponding to that z-score.

Let's calculate the z-score and then determine the area.The calculated z-score is approximately $ z = 2.19 $.

Now, we need to find the area to the right of this z-score, which represents the probability that a peanut butter jar costs more than $4.25. Using standard normal distribution tables or a calculator, we can find the corresponding cumulative probability for $ z = 2.19 $.

Let's compute the area to the right of this z-score.The area under the normal curve for peanut butter jars costing more than $4.25 is approximately **0.0142**. This means that about 1.42% of the peanut butter jars cost more than $4.25.

Would you like more details on this, or do you have any further questions?

Here are 5 related questions you might find interesting:
1. How would the area change if the price were $4.00 instead?
2. What is the probability of a peanut butter jar costing less than $3.00?
3. How would the z-score formula change if we wanted the area between two prices?
4. How does the standard deviation affect the spread of peanut butter prices?
5. Can you compute the z-score for a jar costing $3.50?

**Tip:** The smaller the standard deviation, the more tightly clustered the data is around the mean.

A quick survey of peanut butter prices had standard deviation and mean of $0.26 and $3.68, respectively. Compute the area for a peanut butter jar costing more than $4.25.

Learn how to calculate the area under a normal distribution curve for peanut butter prices. This problem involves finding the probability that a jar costs more than $4.25, using a mean of $3.68 and standard deviation of $0.26.

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