Marketing and Consumer Behavior
A toy manufacturer routinely tests new toys in a controlled environment before deciding whether to actually market a toy. Research has shown that the amount of time (in minutes) a randomly selected child plays with a new toy has an exponential distribution with λ = 0.05. Suppose a new toy is presented for study.
a. What is the probability that a randomly selected child will play with the toy for at most 10 minutes?
b. What is the probability that a randomly selected child will play with the toy for between 5 and 20 minutes?
c. Suppose a child plays with the toy for at least 15 minutes.
What is the probability that the child will play with the toy for another 20 minutes?
d. If four different children each play independently with a new toy for at least 25 minutes, then the toy is immediately brought to market. What is the probability of this happening for a newly designed toy?