a) Market research has shown that 60% of persons who are introduced to a certain product actually buy the product. A random sample of 15 persons were introduced to the product. i) Define the variable...

a) Market research has shown that 60% of persons who are introduced to a certain product actually buy the product. A random sample of 15 persons were introduced to the product.

i) Define the variable of interest for this scenario.

ii) What probability distribution do you think best describes the situation? Why?

iii) Calculate the probability that exactly 9 will buy the product.

iv) If 80 persons are introduced to the product, determine the number of persons who are expected to buy the product.

b) It is known that an average of 5 trains pass through Grand Central Terminal every 30 minutes. Find the probability that

i) Exactly 4 trains will pass in 30 minutes

ii) less than 2 trains will pass in an hour

*In reference to iv) to  b ii)