PROBLEM:
A large corporation has thousands of employees. The distribution of annual salaries for the employees is skewed to the right, with a mean of $68,000 and a standard deviation of $18,000. Because business has been good this year, the CEO of the company decides that very employee will receive a $5000 bonus. Let X be the current annual salary of a randomly selected employee before the bonus and Y be the employee's salary after the bonus. Describe the shape, center, and variability of the probability distribution of Y.
PROBLEM:
Employees selling refrigerators at an appliance store make money on commission based on how many refrigerators they sell. The number of refrigerators R sold in a randomly selected hour has the following probability distribution:
Here is a histogram of the probability distribution along with the mean and standard deviation.
At this appliance store, the commission earned is $30 for each refrigerator sold. That is, if C = total commission earned for a randomly selected hour, C = 30R.
(a) What shape does the probability distribution of C have?
(b) Find the mean of C.
(c) Calculate the standard deviation of C.
PROBLEM:
In a large introductory statistics class, the distribution of scores on a recent test follows an approximately Normal distribution with a mean of 82.4 and a standard deviation of 5.1. Let X be the test score for a randomly selected student. To test the students' grasp of the material, the teacher cleverly decides to convert all the scores to z-scores and then report these values to students. If Z is the z-score for the randomly selected student, then
Z=(X-82.4)/5.1
(a) Find the mean of Z.
(b) Calculate and interpret the standard deviation of Z.
Extracted text: * probabilit XVWLTE (98o 335) VTLEBAVAEEX Section 6.2 Alternate Examples EXILS CLGGIC ALTERNATE EXAMPLE (page 384) Everyone gets a bonus Effect of adding/subtracting a constant PROBLEM: per A large corporation has thousands of employees. The distribution of annual salaries for the employees is skewed to the right, with a mean of $68,000 and a standard deviation of $18,000. Because business has been good this year, the CEO of the company decides that every employee will receive a $5000 bonus. Let X be the current annual salary of a randomly selected employee before the bonus and Y be the employee's salary after the bonus. Describe the shape, center, and variability of the probability distribution of Y. aoismsl blo- ALTERNATE EXAMPLE (page 385) Selling cars wwollat Effect of multiplying/dividing by a constantog eE lo noltal 30 bon PROBLEM: 18 rue Employees selling refrigerators at an appliance store make money on commission based on how many refrigerators they sell. The number of refrigerators R sold in a randomly selected hour has the following probability distribution: Number of 0 1 2 3 4 5 refrigerators Probability 0.22 0.31 0.12 0.25 0.08 0.02 Here is a histogram of the probability distribution along with the mean and standard deviation.
Extracted text: (b) Describe P(X>0) in w ds and find its value. ty. 30- 0.25 0.20 0.15 a10 00'0 0 1 2 3 4 5 R = Number of refrigerators sold HR= 1.72 %3D OR= 1.36 At this appliance store, the commission earned is $30 for each refrigerator sold. That is, if C = total commission earned for a randomly selected hour, C = 30R. (a) What shape does the probability distribution of C have? (b) Find the mean of C. (c) Calculate the standard deviation of C. 20 ALTERNATE EXAMPLE (387) What z-score did I get? Analyzing the effect of transformations PROBLEM: In a large introductory statistics class, the distribution of scores on a recent test follows an approximately Normal distribution with a mean of 82.4 and a standard deviation of 5.1. Let X be the test score for a randomly selected student. To test the students' grasp of the material, the teacher cleverly decides to convert all the scores to z-scores and then report these values to students. If Z is the z-score for the randomly selected student, then X-82.4 5.1 (a) Find the mean of Z. (b) Calculate and interpret the standard deviation of Z.