In grading eggs into medium and large cartons, a poultry farm packs "medium" cartons that have an average weight of 250 ounces with a standard deviation of 70 ounces. Cartons that are marked "large" have an average weight of 280 ounces with a standard deviation of 40 ounces.Assume that the distribution of the weights is normal.What is the weight of the top 2.5% of the large cartons?What is the probability that the mean weight of 60 randomly selected medium cartons is less than the mean weight of 55 randomly selected large cartons?If a day's packaging contained 60.5% of large eggs, what is the probability that in a random sample of 100 cartons, more than half of the cartons contain large eggs?A single numerical value used as an estimate of a population parameter is known asi. a population parameterii. a mean estimatoriii. a parameteriv. None of the above

Solution:-1. Weight of the Top 2.5% of Large CartonsTo find the weight of the top 2.5% of large…

Answered: In grading eggs into medium and large…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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In grading eggs into medium and large cartons, a poultry farm packs "medium" cartons that have an average weight of 250 ounces with a standard deviation of 70 ounces. Cartons that are marked "large" have an average weight of 280 ounces with a standard deviation of 40 ounces.

Assume that the distribution of the weights is normal.

What is the weight of the top 2.5% of the large cartons?
What is the probability that the mean weight of 60 randomly selected medium cartons is less than the mean weight of 55 randomly selected large cartons?
If a day's packaging contained 60.5% of large eggs, what is the probability that in a random sample of 100 cartons, more than half of the cartons contain large eggs?
A single numerical value used as an estimate of a population parameter is known as

i. a population parameter

ii. a mean estimator

iii. a parameter

iv. None of the above

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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