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 40 ​ten-gram portions of the food item is obtained and results in a sample mean of x=5.5 insect fragments per​ ten-gram portion. Complete parts​ (a) through​ (c) below.   Click here to view the standard normal distribution table (page 1). LOADING... Click here to view the standard normal distribution table (page 2). LOADING... ​(a) Why is the sampling distribution of x approximately​ normal?     A. The sampling distribution is approximately normal because the population is normally distributed and the sample size is large enough.   B. The sampling distribution is assumed to be approximately normal.   C. The sampling distribution is approximately normal because the popluation is normally distributed.   D. The sampling distribution is approximately normal because the sample size is large enough. Your answer is correct.   ​(b) What is the mean and standard deviation of the sampling distribution of x assuming μ=5 and σ=5​?   μx= ​(Round to three decimal places as​ needed.)     Enter your answer in the answer box and then click Check An

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Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.