**Understanding Salary Distributions for MBA Graduates**Business Weekly conducted a survey of graduates from 30 top MBA programs. Based on the survey, assume the mean annual salary for graduates 10 years after graduation is $152,000. Assume the standard deviation is $45,000. Suppose you take a simple random sample of 48 graduates. Round all answers to four decimal places if necessary.**Questions and Answers:**a. **What is the distribution of $ X $?** \[ X \sim N(152,000, 45000) \]b. **What is the distribution of $ \overline{X} $?** \[ \overline{X} \sim N(152,000, \frac{45000}{\sqrt{48}}) \]c. **For a single randomly selected graduate, find the probability that her salary is between $142,257 and $147,705.**d. **For a simple random sample of 48 graduates, find the probability that the average salary is between $142,257 and $147,705.**e. **For part d), is the assumption of normal necessary?** \[ \text{Yes} \]In these questions:1. $ X $ represents the salary of a single MBA graduate.2. $ \overline{X} $ represents the average salary of a sample of 48 MBA graduates.3. $ N(\mu, \sigma) $ represents a normal distribution with mean $ \mu $ and standard deviation $ \sigma $.**Explanation of Formulas:**1. **Distribution of $ X $**: - $ X $ follows a normal distribution $ N $ with a mean $ \mu = \$152,000 $ and a standard deviation $ \sigma = \$45,000 $.2. **Distribution of $ \overline{X} $**: - The distribution of the sample mean $ \overline{X} $ also follows a normal distribution, but with a standard deviation adjusted by the square root of the sample size $ n = 48 $.3. **Probability Calculations**: - The probabilities require using the properties of the normal distribution, typically by converting to the standard normal distribution (z-scores).4. **Assumption of Normality**: - The assumption of normality is

Given: Mean = $152000 Standard deviation = $12000 Sample size = 45

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 $132,000. Assume the standard deviation is $31,000. Suppose you take a simple random sample of 37 graduates. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N( b. What is the distribution of ? I - N c. For a single randomly selected graduate, find the probability that her salary is between $129,255 and $133,703. d. For a simple random sample of 37 graduates, find the probability that the average salary is between $129,255 and $133,703. e. For part d), is the assumption of normal necessary? O YesO No
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 $178,000. Assume the standard deviation is $39,000. Suppose you take a simple random sample of 36 graduates. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N( b. What is the distribution of I? I - N( c. For a single randomly selected graduate, find the probability that her salary is between $173,350 and $181,100. d. For a simple random sample of 36 graduates, find the probability that the average salary is between $173,350 and $181,100. e. For part d), is the assumption of normal necessary? O NoO Yes o
Scores on an aptitude test are normally distributed with a mean of 960 and standard deviation of 120. Use the Cumulative Z-Score Table to answer the following questions. Write your answer rounded to the nearest whole number. If 1,570,000 students take the test.. how many would you expect to score above 1224? students ...how many would you expect to score above 972? students ...how many would you expect to score between 972 and 1224? students
M2
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 $181,000. Assume the standard deviation is $32,000. Suppose you take a simple random sample of 39 graduates. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N b. What is the distribution of a? - NO c. For a single randomly selected graduate, find the probability that her salary is between $180,714 and $188,276. d. For a simple random sample of 39 graduates, find the probability that the average salary is between $180,714 and $188,276. e. For part d), is the assumption of normal necessary? O No Yes Question Help: Message instructor Submit Question
A survey was conducted two years ago asking college students their top motivations for using a credit card. To determine whether this distribution has changed, you randomly select 425 college students and ask each one what the top motivation is for using a credit card. Can you conclude that there has been a change in the claimed or expected distribution? Use a=0.10. Complete parts (a) through (d). New Survey Frequency, f 111 97 Response Old Survey % Rewards 29% 23% Low rates Cash back Discounts Other 22% 108 8% 46 18% 63 UD. XX O D. X Xo 2 OC. X >Xo OC. X>x (c) Calculate the test statistic. (Round to three decimal places as needed.) %3D (d) Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. V the claimed or ▼enough evidence to conclude that the distribution of motivations Ho At the 10% significance level, there expected distribution.
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 $132,000. Assume the standard deviation is $31,000. Suppose you take a simple random sample of 37 graduates. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N( 132000 31000 b. What is the distribution of ? T - N( 132000 c. For a single randomly selected graduate, find the probability that her salary is between $129,255 and $133,703. 0.0558 d. For a simple random sample of 37 graduates, find the probability that the average salary is between 5096.3686 $129,255 and $133,703. e. For part d), is the assumption of normal necessary? YesO No o
On average, accountants earn approximately an average of $6500 per year in the United States. Assume that the distribution for electricians’ yearly earnings is normally distributed and that the standard deviation is $8680. Given a sample of 64 electricians, what is the standard deviation for the sampling distribution of the sample mean? a. 1205 b. 8680 c. 6000 d. 1085
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 $178,000. Assume the standard deviation is $39,000. Suppose you take a simple random sample of 36 graduates. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N( 178000 39000 b. What is the distribution of ? T - N( 178000 c. For a single randomly selected graduate, find the probability that her salary is between $173,350 and $181,100. 0.0791 6500 d. For a simple random sample of 36 graduates, find the probability that the average salary is between $173,350 and $181,100. e. For part d), is the assumption of normal necessary? NoO Yes o
A study investigating the relationship between age and annual medical expenses randomly samples 100 individuals in a city. It is hoped that the sample will have a similar mean age as the entire population. If the standard deviation of the ages of all individuals in the city is σ = 20, find the probability that the mean age of the individuals sampled is within 1.5 years of the mean age for all individuals in the city. Do not round your answer. Hints: Find the sampling distribution of the sample mean age and use the central limit theorem. You don’t have to know the population mean to answer this, but if it makes it easier, use a value such as μ=35.

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