Find the probability that the total weight of the sacks of potatoes in a crate exceeds 500 kg.

To answer the question on the probability that the total weight of the sacks of potatoes in a crate exceeds 500 kg, we need to make certain assumptions about the distribution of the weights of the sacks. Let's assume:

• The weights of the sacks are normally distributed.
• We have information about the mean weight ($\mu$) and standard deviation ($\sigma$) of the weights of the sacks.

Step 1: Break Down the Problem

1. Let's denote:

   • $X$: Total weight of sacks.
   • $n$: Number of sacks.
   • Each sack has a weight that follows $\mathcal{N}(\mu, \sigma^2)$.

2. The total weight $X$ will be the sum of the weights of the individual sacks.

3. We want to find $P(X > 500)$.

Step 2: Relevant Concepts

1. The sum of normally distributed random variables is also normally distributed. Thus: $X \sim \mathcal{N}(n\mu, n\sigma^2)$

2. To find $P(X > 500)$, we standardize $X$ to find the Z-score: $Z = \frac{X - \text{mean}}{\text{standard deviation}} = \frac{X - n\mu}{\sqrt{n}\sigma}$

Step 3: Analysis and Detail

1. We can rewrite the probability: $P(X > 500) = P\left(Z > \frac{500 - n\mu}{\sqrt{n}\sigma}\right)$

2. To find this probability, we will need to find the corresponding Z value. Then we can look up the value in the Z-table or use a normal distribution calculator.

Step 4: Verify and Summarize

1. Compare the computed Z-value to the standard normal distribution to find the probability.

Final Answer

Without exact values for $n$, $\mu$, and $\sigma$, the answer cannot be computed numerically. However, the procedure to find the probability $P(X > 500)$ follows the above steps.

• Please provide the mean weight, standard deviation, and the number of sacks to calculate the specific probability.