Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $126,000. Assume the standard deviation is $31,000. Suppose you take a simple random sample of 40 graduates. Round all answers to four decimal places if necessary.What is the distribution of �? � ~ N(,)What is the distribution of �¯? �¯ ~ N(,)For a single randomly selected graduate, find the probability that her salary is between $119,648 and $123,199. For a simple random sample of 40 graduates, find the probability that the average salary is between $119,648 and $123,199. For part d), is the assumption of normal necessary? YesNo

The objective of the question is to understand the distribution of the salaries of MBA graduates and…

Answered: Business Weekly conducted a survey of…

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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Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $126,000. Assume the standard deviation is $31,000. Suppose you take a simple random sample of 40 graduates. Round all answers to four decimal places if necessary.

What is the distribution of �? � ~ N(,)
What is the distribution of �¯? �¯ ~ N(,)
For a single randomly selected graduate, find the probability that her salary is between $119,648 and $123,199.
For a simple random sample of 40 graduates, find the probability that the average salary is between $119,648 and $123,199.
For part d), is the assumption of normal necessary? YesNo

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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