A grocery store produce manager is told by a wholesaler that the apples in a large shipment have a mean weight of 7 ounces and standard deviation of 1.8 ounces. The manager is going to randomly select 36 apples and is willing to risk a 1.5% chance of returning the shipment , (a) assuming the wholesaler’s claim is true, what is the probability that the sample mean weight of 36 apples falls below the cutoff X bar ounces. Find X bar. (b) Find the probability that the sample mean weight (X bar) falls above 6.55 ounces. (c) The new manager decides to return the shipment if the sample mean weight is less than 6.4 ounces. Find the probability that the shipment of apples will be returned. Assume that the wholesaler’s claim is true.

Given that the mean weight of 7 ounces and standard deviation of 1.8 ounces. That is, μ=7 and σ =…

Answered: A grocery store produce manager is told…

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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A grocery store produce manager is told by a wholesaler that the apples in a large shipment have a mean weight of 7 ounces and standard deviation of 1.8 ounces. The manager is going to randomly select 36 apples and is willing to risk a 1.5% chance of returning the shipment , (a) assuming the wholesaler’s claim is true, what is the probability that the sample mean weight of 36 apples falls below the cutoff X bar ounces. Find X bar. (b) Find the probability that the sample mean weight (X bar) falls above 6.55 ounces. (c) The new manager decides to return the shipment if the sample mean weight is less than 6.4 ounces. Find the probability that the shipment of apples will be returned. Assume that the wholesaler’s claim is true.

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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