The acceptable level for insect filth in a certain food item is 5 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 50 ten-gram portions of the food item is obtained and results in a sample mean of $\bar{x}=5.8$ insect fragments per ten-gram portion. Complete parts (a) through (c) below. What is the probability a simple random sample of 50 ten-gram portions of the food item results in a mean of at least 5.8 insect fragments? $P(\bar{x} \geq 5.8)=0.0057$ (Round to four decimal places as needed) Is this result unusual? A. This result is unusual because its probability is large. B. This result is not unusual because its probability is small. C. This result is unusual because its probability is small. D. This result is not unusual because its probability is large.

Step 1 ：The acceptable level for insect filth in a certain food item is 5 insect fragments per 10 grams. A simple random sample of 50 ten-gram portions of the food item is obtained and results in a sample mean of \(\bar{x}=5.8\) insect fragments per ten-gram portion.

Step 2 ：We are asked to find the probability that a simple random sample of 50 ten-gram portions of the food item results in a mean of at least 5.8 insect fragments. The given probability is 0.0057.

Step 3 ：\(P(\bar{x} \geq 5.8)=0.0057\) (Round to four decimal places as needed)

Step 4 ：We are also asked to determine whether this result is unusual. In statistics, a result is considered unusual if its probability is less than or equal to 0.05.

Step 5 ：We compare the given probability (0.0057) with 0.05 to determine if the result is unusual or not.

Step 6 ：Since 0.0057 is less than 0.05, we conclude that the result is unusual because its probability is small.

Step 7 ：\(\boxed{\text{The correct answer is C. This result is unusual because its probability is small.}}\)