Answered: An orange juice producer buys oranges…

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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Question

An orange juice producer buys oranges from a large orange grove that has one variety of orange. The amount of juice squeezed from these oranges is approximately normally distributed, with a mean of 4.20 ounces and a standard deviation of 0.20 ounce. Suppose that you select a sample of 16 oranges.

a. What is the probability that the sample mean amount of juice will be at least 4.14 ounces?

b. The probability is 74% that the sample mean amount of juice will be contained between what two values symmetrically distributed around the population mean?

c. The probability is 75% that the sample mean amount of juice will be greater than what value?

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 + ...

Expert Solution

Step 1

Mean(µ) = 4.20
Standard deviations (σ) = 0.20

n = 16

the mean and standard deviation of the sample mean is given by
Mean= µ_x̅ = µ = 4.20
Standard deviation(σ_x̅) = σ/√n= 0.20/√16 =0.05
Standard deviation(σ_x̅) = 0.05