Question

Scientists have invented a portable testing machine for a new virus that runs on rechargeable batteries. For any given machine, the time (in minutes) it takes to be fully charged is uniformly distributed. The expected time it takes a machine to be fully charged is unknown but the variance is known to be 48. Further, it is known that 45% of these machines will be fully charged in less than 109 minutes. Find the expected time it takes for a portable testing machine to be fully charged.

Answer 1

The distribution is uniform

say U[a,b]

V(x) = 48

Now,

Here, at x = 109 F(x) = 45% = 0.45