After measuring the duration of many telephone calls, the telephone company found their data was well-approximated by the density function p(x) = 0.4e^(−0.4x), where x is the duration of a call, in minutes.
a) What percentage of calls last between 4 and 5 minutes? (nearest tenth)
b) What percentage of calls last 4 minutes or less? (nearest tenth)
c) What percentage of calls last 4 minutes or more? (nearest tenth)

a)

b)

c)

Step-by-step explanation:

For this case we define the random variable X who represent the duration of a call, in minutes, and the density function for X is given by:

Part a

For this case we want to find this probability:

And we can find this probability with this integral:

Part b

Part c

For this case we want this probability:

And we can use the complement rule and the result from part b and we got:

you need to show the graph

step-by-step explanation: