Computers crash due to errors in the programs written by coders, and developers fix these issues, with each fix requiring a random amount of time. If you can answer the question without simulation, please do so. If you cannot answer the question without simulation (i.e., you require using replicate), please use 1000 simulations.

a. Suppose that computer crash occur at a rate of 1 every two hours. What is the probability that more than 4 crashes occur in an eight-hour working period?

b. Every time a computer crashes, it is observed that at least one program is affected. The additional number of programs affected is a random number which follows a binomial distribution with size 4 and probability 0.5 (so that number of programs affected is 1,2,3,4 or 5). What is the probability mass function for the number of programs affected for a randomly chosen crashed computer?

c. What is the expected number of programs identified as affected in an eight-hour work day?

d. Given that the amount of time that is required to fix a program can be modeled as a normally distributed random variable with mean 30 min and standard deviation 10 min, and that the hourly rate that the developers charge is $150, what is the expected amount of money that must be spent on developers in a work week which consists of 5 eight-hour days?

e. What is the 25th percentile of the weekly spend distribution identified in part d?