New legislation passed in 2017 by the U.S. Congress changed tax laws that affect how many people file their taxes in 2018 and beyond. These tax law changes will likely lead many people to seek tax advice from their accountants (The New York Times). Backen and Hayes LLC is an accounting firm in New York state. The accounting firm believes that it may have to hire additional accountants to assist with the increased demand in tax advice for the upcoming tax season. Backen and Hayes LLC has developed the following probability distribution for x = number of new clients seeking tax advice. Excel File: data05-19.xlsx a. Is this a valid probability distribution? Yes Explain. f(x) greater than or equal to 0 f(2) equal to 1 x f(x) 20 0.05 25 0.20 30 0.25 35 0.15 40 0.15 45 50 48 0.10 0.10 b. What is the probability that Backen and Hayes LLC will obtain 40 or more new clients (to 2 decimals)? c. What is the probability that Backen and Hayes LLC will obtain fewer than 35 new clients (to 2 decimals)? d. Compute the expected value, variance, and standard deviation of (to 2 decimals). Expected value Variance Standard Deviation The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied). Excel File: data05-21.xlsx Probability Job Satisfaction IS Senior IS Middle Score Executives Managers 1 0.05 0.04 2 0.09 0.10 3 0.03 0.12 4 0.42 0.46 5 0.41 0.28 a. What is the expected value of the job satisfaction score for senior executives (to 2 decimals)? b. What is the expected value of the job satisfaction score for middle managers (to 2 decimals)? c. Compute the variance of job satisfaction scores for executives and middle managers (to 2 decimals). Executives Middle managers d. Compute the standard deviation of job satisfaction scores for both probability distributions (to 2 decimals). Executives Middle managers e. What comparison can you make about the job satisfaction of senior executives and middle managers? Senior executives have higher satisfaction with more variation