The amount of time that a mobile phone will work without having to be recharged is a random variable having the Exponential distribution with mean 3.33.3 days.

a) Find the probability that such a mobile phone will have to be recharged in less than 1.51.5days.

(Enter your answer correct to 3 decimal places)

b) Suppose a new model of phone has probability 0.29220.2922 of needing to be recharged in less than 1.51.5days. We have 2020 of these new phones, all put in usage on the same day and working independently of each other.

Use Matlab to find the probability that at least 66 of them will have to be recharged in less than 1.51.5days.

(Enter your answer correct to 3 decimal places)