A company maintains three offices in a certain region, each staffed by two employees. Information concerning yearly salaries (in thousands of dollars) is as follows:| Office | Employee | Salary ||--------|----------|--------|| 1 | 1 | 20.7 || 1 | 2 | 24.6 || 2 | 3 | 21.2 || 2 | 4 | 24.6 || 3 | 5 | 16.8 || 3 | 6 | 20.7 |**(a)** Suppose two of these employees are randomly selected from among the six (without replacement). Determine the sampling distribution of the sample mean salary $ \overline{X} $. (Enter your answers for $ p(\overline{x}) $ as fractions.)\[\begin{array}{c|c|c|c|c|c}\overline{x} & 18.75 & 20.70 & 20.95 & 22.65 & 24.60 \\\hlinep(\overline{x}) & \frac{1}{15} & & & \frac{2}{15} & \\\end{array}\]**(b)** Suppose one of the three offices is randomly selected. Let $ X_1 $ and $ X_2 $ denote the salaries of the two employees. Determine the sampling distribution of $ \overline{X} $. (Enter your answers as fractions.)\[\begin{array}{c|c|c|c}\overline{x} & 18.75 & 22.65 & 22.90 \\\hlinep(\overline{x}) & 0.3333 & 0.3333 & 0.3333 \\\end{array}\]### Explanation of Graphs/Diagrams1. **Table of Salaries**: - Displays the salaries of employees across three offices. Each office has two employees with specified salaries.2. **Sampling Distribution for Part (a)**: - A series of mean salary values $ \overline{x} $ that could result from randomly picking two employees. - Their corresponding probabilities $ p(\overline{x}) $ given as fractions

a) Create a table with all the possible pairs of average salaries. Employee 1 Employee 2 Salary…

Answered: A company maintains three offices in a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Auto Loans-George works for a credit union that serves a large, urban area. For his annual report, he wants to estimate the mean interest rate for 60- month fixed-rate auto loans at lending institutions (banks, credit unions, auto dealers, etc.) in his area. George selects a random sample of 12 lending institutions and obtains the following rates: 3.79 5.01 5,16 3.12 4.49 5.02 n = 5.58 4.08 4.01 7.02 4.33 3.64 Round all calculated answers to 4 decimal places. George calculates a sample mean of 4.6042 and a sample standard deviation of 1.0421. 1. Calculate a 90% confidence interval for the mean interest rate for 60-month fixed-rate auto loans at lending institutions in George's area. Assume necessary conditions have been met and round your result to 4 decimal places. After calculating the interval, George decides he wants to estimate the interest rate for 60-month fixed-rate auto loans at 90% confidence with a margin of error of no more than 0.13. 2. Using George's initial sample…
Teacher salaries. Suppose that teachers at a university in the USA - with the rank of professor in public institutions offering two-year academic programs - earn an average of $71,802 per year, with a standard deviation of $4,000. In an attempt to verify this salary level, a random sample of 60 professors was selected from a database of academic staff from all public institutions offering two-year programs in the USA. a. Describe the sampling distribution of the sample mean X. b. Within what limits would you expect the sample mean to lie, with a probability of 0.95? c. Calculate the probability that the sample mean x is greater than $73,000. d. If a random sample actually produced a sample mean of $73,000, would you consider this to be uncommon? What conclusion would you draw?
The Census Bureau gives this distribution for the number of people in American households in 2016. Family size 1 2 4 6. 7 Proportion 0.28 0.35 0.15 0.13 0.06 0.02 0.01 Note: In this table, 7 actually represents households of size 7 or greater. But for purposes of this exercise, assume that it means only households of size exactly 7. Suppose you take a random sample of 4000 American households. About how many of these households will be of size 2? Sizes 3 to 7? The number of households of size 2 is about The number of households of size 3 to 7 is about
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In a survey about the use of annual pass to a theme park, each interviewee is asked about the number of visits to the theme park in a year. Below is the result from 500 randomly selected annual pass card holders. Number of visits 3 4 5 6 7 8 Number of interviewees 52 165 110 88 55 30 (a) Find the point estimate of the population proportion of annual pass holders have visited the theme park at least 6 times in a year. (b) Calculate the sampling error at 95% confidence level. (c) Construct a 95% confidence interval estimate of the population proportion of annual pass holders have visited the theme park at least 6 times in a year.
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The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts (a) and (b) below. Actress (years) 31 29 34 28 34 26 28 Actor (years) 59 40 39 40 30 32 54 a. Use the sample data with a 0.05 significance level to test the claim that for the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0 (indicating that the Best Actresses are generally younger than Best Actors). In this example, is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the actress's age minus the actor's age. What are the null and alternative hypotheses for the hypothesis test? Ho: Ho Md 42 27 33 40 41 43 year(s) year(s) H₁ H (Type integers or decimals. Do not round.) Identify the…
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