The acceptable level for insect filth in a certain food item is 3 insect fragments​ (larvae, eggs, body​ parts, and so​ on) per 10 grams. A simple random sample of 40 ​ten-gram portions of the food item is obtained and results in a sample mean of x=3.8 insect fragments per​ ten-gram portion. ​(c) What is the probability a simple random sample of 40 ​ten-gram portions of the food item results in a mean of at least 3.8 insect​ fragments? ​P (x≥3.8​) =

What position in the distribution corresponds to a z-score of z = +2.00?​

Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 4.0 minutes and standard deviation of 2.0 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 46 customers in the first line and n₂ = 52 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X₁ and the mean service time for the longer one X₂ is more than 0.3 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = !

A particular fruits’ weights are normally distributed, with a mean of 312 grams, and a SD of 20 grams. If you pick 6 fruits at random, then 16% of the time, their mean weight will be greater than how many grams? (Give the answer to the nearest gram)