Answered: The number of chocolate chips in an…

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 number of chocolate chips in an 18-ounce bag of Chips Ahoy! Chocolate cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips according to a study by the U.S. Air Force Academy.

If a production manager takes a sample of 36 bags of cookies, then for this sample size, describe the sampling distribution of x ¯ .

i. Center: μ x ¯ = 1262

ii. Spread: σ x ¯ = 19.67

iii. What is the probability that a simple random sample of 36 bags results in a sample mean of at least 1275 chocolate chips? .746

iv. Interpret the probability from above “If 1000 samples of size 36 bags were obtained from this population, we would expect sample(s) to have a sample mean of at least 1275.” (round to the nearest whole number)

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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