Mergers and slow periods in the economy often result in layoffs at many firms. Many employees count on two or three months of severance pay to carry them over to the next job. However, job searches can sometimes take longer than 6 months. A survey of workers who have been with firms for more than a year revealed that only 30% of the workers would be financially secure if they lost their jobs for 6 months to a year. Let X represents the number of employees out of a sample of 80 who would feel financially secure if they lost their job for 6 months to a year.

a) What is the probability that at least 30 employees out of 80 would be financially secure if they lost their job for 6 months to a year?

b) Do a what-if analysis by changing the probability to .4, and .5, and rework part a).