Answered: A certain type of candy has a mean…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A certain type of candy has a mean weight of 0.1 ounces and a standard deviation of 0.015 ounces. A bag labeled as 12-ounce contains 120 candies and is supposed to weigh at least 11.9 ounces. However, the manufacturer would be willing to accept it if up to 10% of their bags weight less than 11.9 ounces.

What is the probability that such a sample of 120 candies weighs less than 11.9 ounces? (Or formulated differently, what is the probability that a sample of 120 candies has a sample mean of less than

ounces?)
First find the mean and standard deviation (round to 5 decimal places) of the sampling distribution of the sample mean and verify that said sampling distribution is approximately normal.

Will they manufacturer be ok with how their bags are currently filled? If not, what could they change?

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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