The acceptable level for insect filth in a certain food item is 2insect 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 x=2.5 insect fragments per ten-gram portion. Complete parts (a) through (c) below. The acceptable level for insect filth in a certain food item is 2 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 50ten-gram portions of the food item is obtained and results in a sample mean of x = 2.5 insect fragments per ten-gram portion. Complete parts (a) through (c) below.A. The sampling distribution of x is approximately normal because the sample size is large enough.B. The sampling distribution of x is assumed to be approximately normal.C. The sampling distribution of x is approximately normal because the population is normally distributed.O D. The sampling distribution of x is approximately normal because the population is normally distributed and the sample size is large enough.(b) What is the mean and standard deviation of the sampling distribution of x assuming µ = 2 and o =/2?= 2 (Round to three decimal places as needed.)o; = 0.2 (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 results in a mean of at least 2.5 insect fragments?P(x22.5) =|(Round to four decimal places as needed.)

Sampling distribution of sample mean(x¯) : Suppose simple random sample of size ‘n’ is drawn from…

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The acceptable level for insect filth in a certain food item is 2insect 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 x=2.5 insect fragments per ten-gram portion. Complete parts (a) through (c) below.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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