Suppose the average number of tax returns processed by the IRS employees is 14 per day with a standard deviation of 5 per day. 38 employees are randomly sampled.What is the probability of taking a random sample of 38 employees and having the resulting mean number of returns processed per day be greater than 15? The company wants a random sample of 38 employees yields a mean of at least 15 returns processed per day 30% of the time. What must the mean tax returns processed per day be to achieve that goal? (Assume the standard deviation remains the same.)

Given information:1) To find the probability of taking a random sample of 38 employees and having the resulting mean number of returns processed per day be greater than 15 that is to find The probability of taking a random sample of 38 employees and having the resulting mean number of returns processed per day be greater than 15 is 0.10882) To find the mean tax returns processed per day be to achieve that goal such that The mean tax returns processed per day be to achieve that goal is 13.5747 1)The probability of taking a random sample of 38 employees and having the resulting mean number of returns processed per day be greater than 15 is 0.10882) The mean tax returns processed per day be to achieve that goal is 13.5747

Answered: Suppose the average number of tax…

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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Suppose the average number of tax returns processed by the IRS employees is 14 per day with a standard deviation of 5 per day. 38 employees are randomly sampled.
1. What is the probability of taking a random sample of 38 employees and having the resulting mean number of returns processed per day be greater than 15?

The company wants a random sample of 38 employees yields a mean of at least 15 returns processed per day 30% of the time. What must the mean tax returns processed per day be to achieve that goal? (Assume the standard deviation remains the same.)

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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