(Solved): complete a through c please. ulti The acceptable level for insect fith in a certain food item is 2 i ...

The acceptable level for insect fith in a certain food item is 2 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 50 ten-gram portions of the food iem is obtained and results in a sample mean of $\bar{x}=2.5$ insect tragments per ten-gram portion. Complete parts (a) through (c) below. (a) Why is the sampling distribution of $\bar{x}$ approximately normal? A. The sampling distribution of $\hat{x}$ is approximately normal because the population is normally distributed B. The sampling distribution of $\bar{x}$ is approximately normal because the population is normally distributed and the sample size is large enough. C. The sampling distribution of $\bar{x}$ is assumed to be approximately normal. D. The sampling distribution of $\bar{x}$ is approximately normal because the sample size is large enough. (b) What is the mean and standard deviation of the sampling distribution of $\bar{x}$ assuming $\mu =2$ and $\sigma =\sqrt{2}$ ? ${\mathrm{H}}_{\mathrm{x}}=$ (Round to three decimal places as needed.) ${\sigma }_{\ast }=$ (Round to three decimal places as needed.) (c) What is the probability a simple random sample of 50 ten-gram portions of the food item rosults in a mean of at least 2.5 insect fragments? $P(\bar{x}\ge 2.5)=$ (Round to four decimal places as needed.) Is this result unusual? A. This result is not unusual because its probability is greater than 0.05 B. This result is not unusual because its probability is less than 0.05 C. This result is unusual because its probability is less than 0.05 D. This result is unusual because its probability is greater than 0.05