A remote operated vehicle detects debris from a sunken craft

A remote operated vehicle detects debris from a sunken craft at a rate of 50 pieces per hour. The time to detect debris can be modeled using an exponential distribution.

(a) What is the probability that the time to detect the next piece of debris is less than 2 minutes?

(b) What is the probability that the time to detect the next piece of debris is between 2.5 and 4.5 minutes?

(c) What is the expected number of detected pieces of debris in a 20-minute interval?

(d) Now use your answer from part c to answer: what is the probability tht 10 pieces of debris are found in a 20 minute interval?

Solution

=50 pieces/hour 0.833 pieces&/minute

a) P<= 2 minute = 1- = 0.8109

b) P(2.5 <x<4.5)

P<= 2.5minute = 1- = 0.875

P<= 4.5 minute = 1- = 0.9754

P(2.5 <x<4.5)= 0.9754-0.875=0.1004

c) 20 minutes and you can make 0.833 pieces /minute = 20*0.833=16.66 aprox =16

d) the probability is 100% because you have the capacity to make more than 10