Sample annual salaries (in thousands of dollars) for employees at a company are listed.

$$48, 45,62,59,32,32,48,45,62,26,59,48,49.$$

Each employee in the sample is given a $5\%$ raise. Find the sample mean and sample standard deviation for the revised data set.

The following are the current annual salaries (in thousands of dollars) for the starting players on the Miami Heat basketball team: 14,500, 14,500, 14,000, 5000, 3500.

a. Find the mean $\bar{x}$ and express the result in dollars instead of thousands of dollars.

b. Find the median and express the result in dollars instead of thousands of dollars.

c. Find the standard deviations and express the result in dollars instead of thousands of dollars.

d. Find the variance $s^2$ and express the result in appropriate units.

e. Convert the first salary of $\$ 14,500,000$ to a $z$ score.

f. What level of measurement (nominal, ordinal, interval, ratio) describes this data set?

g. Are the salaries discrete data or continuous data?

h. Do the given salaries appear to be representative of all players for the Miami Heat team? Why or why not?

The table shows the average annual salaries y (in thousands of dollars) for public school classroom teachers in the United States from 2002 to 2004.

(a) Use the equation of the parabola $y=a t^2+b t+c$ to estimate the average annual salaries in 2005, 2010, and 2015.

(b) Are your estimates in part (a) reasonable Explain.

Annual salary plus bonus data for chief executive officers are presented in the $BusinessWeek$ Annual Pay Survey. A preliminary sample showed that the standard deviation is $\$675$ with data provided in thousands of dollars. How many chief executive officers should be in a sample if we want to estimate the population mean annual salary plus bonus with a margin of error of $\$100,000$? (Note: The desired margin of error would be $E=100$ if the data are in thousands of dollars.) Use $95\%$ confidence.

Sample annual salaries (in thousands of dollars) for employees at a company are listed.

$$43, 46, 57, 47, 34, 34, 43, 46, 57, 32, 47, 43, 44$$

Find the sample mean and sample standard deviation.

The standard deviation is an imperfect measure of dispersion since it measures absolute variability rather than relative variability. The variability of two independent data sets with various measurement units may occasionally need to be compared. The coefficient of variation is one such measure. The coefficient of variation, denoted by CV, expresses standard deviation as a percentage of the mean and is computed as follows: For population data: $\quad \mathrm{CV}=\dfrac{\sigma}{\mu} \times 100 \%$ For sample data: $\quad \mathrm{CV}=\dfrac{s}{\bar{x}} \times 100 \%$ The yearly salaries of all employees who work for a company have a mean of $62,350 and a standard deviation of$6820. The average number of years of experience for the same employees is 15, with a standard deviation of 2 years. Is the proportionate difference between these employees' years of experience and their wages greater or less than that?

Sample annual salaries (in thousands of dollars) for employees at a company are listed.

$$48, 45, 62, 59, 32, 32, 48, 45, 62, 26, 59, 48, 49.$$

To calculate the monthly salary, divide each original salary by $12$. Find the sample mean and sample standard deviation for the revised data set.

Find the indicated probabilities and interpret the results. If convenient, use technology to find the probabilities. The mean value of land and buildings per acre for farms in Colorado is $1170. A random sample of 32 Colorado farms is selected. What is the probability that the mean value of land and buildings per acre for the sample is (a) less than$1200, (b) more than $1275, and (c) between$1100 and 1250? Assume

$$\sigma = \$ 200$$

.

Find the mean and standard deviation of the population. List all samples (with replacement) of the given size from that population and find the mean of each. Find the mean and standard deviation of the sampling distribution of sample means and compare them with the mean and standard deviation of the population. The numbers of DVDs rented by each of four families in the past month are 8, 4, 16, and 2. Use a sample size of 3.

If a random sample of size 36 is obtained from a population with mean 50 and standard deviation 24, what is the mean and standard deviation of the sampling distribution of the sample mean?

In the earlier exercise, a population and sample size are given. Find the mean and standard deviation of the sampling distribution of sample means and compare them with the mean and standard deviation of the population.

The minutes of overtime reported by each of the three executives at a corporation are 90,120 , and 210. Use a sample size of 3.

A population and sample size are given. (a) Find the mean and standard deviation of the population. (b) List all samples (with replacement) of the given size from the population and find the mean of each. (c) Find the mean and standard deviation of the sampling distribution of sample means and compare them with the mean and standard deviation of the population. The goals scored in a season by the four starting defenders on a soccer team are 1, 2, 0, and 3. Use a sample size of 2.

A population has a mean $\mu$ and a standard deviation $\sigma$. Find the mean and standard deviation of the sampling distribution of sample means with sample size n. $\mu=790, \sigma=48, n=250$

A population has a mean $\mu$ and a standard deviation $\sigma$. Find the mean and standard deviation of the sampling distribution of sample means with sample size n. $\mu=45, \sigma=15, n=100$