Question 1 (5 parts ): A salesperson who sells an appliance to small businesses calls on 4 potential buyers every day . Based on historical information , the probability of making a sale is 12 % for every potential buyer . Potential buyers ' decisions are are assumed to be independent Let the random variable X be the total count of successful sales that the salesperson makes on a given day . a. What is the probability that the salesperson fails to make any sales on a given day ? b. What is the probability that the salesperson makes multiple sales (more than one ) on a given day ? C . If the selling price of the appliance is $999 , what is probability that the revenue from the salesperson's sales exceeds $1000 on a given day ? d. Calculate the expected number and standard deviation of successful sales on a given day . e Assuming again that the selling price of the appliance is $999 , what is the expected revenue from the salesperson's sales for a 5-day workweek ? Question 2 (4 parts ): A software company has undertaken a major project for an important client. The project involves three major phases : design , development , and testing . The amount of time it takes to complete each phase is normally distributed with parameters given in the table below . Phase Mean (4) Standard Deviation ( 5 ) Design 30 weeks 10 weeks Development 45 weeks 15 weeks Testing 8 weeks 2 weeks Assume that the time it takes to complete each phase is independent of the others a . What is the probability that the development phase is completed in less than 52 weeks (i.e., one year )? b. What is the probability that the entire project is completed in less than 78 weeks (i.e., a year and a half )? Hint : the entire project requires the completion of each phase, one after the other . C . What is the probability that the entire project is completed in more than 104 weeks (i.e., two years )? Hint : the entire project requires the completion of each phase , one after the other d. As an incentive for the software company to work faster , the client has offered to pay a $100,000 bonus if the entire project is completed in less than a year and a half , but will charge a $100,000 penalty if the project takes more than two years . Should the software company take this deal ? Briefly explain your