(1)A large 10,000 sq ft office space has 1000 light bulbs. On an average, 5 light bulbs burnout every month and are replaced. Answer the following questions (You must provide the name of the appropriate distribution and give the exact number up to three decimals. Just leaving the formula will not get you any points even though it is correct). You may use R if you want.

a. What is the probability that you need to replace 14 light bulbs in the next month?

b. What is the chance that there will be a four-day gap between two consecutive burnouts? Assume 30 days in a month.

This is a data analytics course, and this was all the material I received to answer the question