Answered: ample of 22 randomly selected accounts,…

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 bank has kept records of the balances of its customers’ account, which is normally distributed with the average daily balance of $500 and standard deviation of $50.

(a) For a sample of 22 randomly selected accounts, what is the distribution of the sample mean? What are the mean, variance and standard deviation of this distribution?

(b) What is the probability that the sample mean of 16 randomly selected accounts will be more than $400?

(d) What is the probability that the sample mean of 36 randomly selected accounts will be between $350 and $400?

(e) If the population of the balances of customers’ accounts is not normally distributed, which, if any, of the questions above can you answer? Justify your answer.

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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