The average time between incoming calls at a
switchboard is 4.5 minutes. The probability of
waiting less than t minutes for next incoming
call is approximated by the model
F(t) = 1 −e^-t/4.5
If a call has just come in, ﬁnd the probability
that the next call will come within a) .51minutes

So do I just plug in .51 minutes in to t? If I do so I get a decimal and it doesn't seem right. Please help explain this.

Question

The average time between incoming calls at a
switchboard is 4.5 minutes. The probability of
waiting less than t minutes for next incoming
call is approximated by the model
F(t) = 1 −e^-t/4.5
If a call has just come in, ﬁnd the probability
that the next call will come within  a) .51minutes  

So do I just plug in .51 minutes in to t? If I do so I get a decimal and it doesn't seem right. Please help explain this.

anonymous · Answer

thats what it says, thats what i would do

anonymous · Answer

i guess you have to change 51 minutes to a decimal first

anonymous · Answer

oh no you don't, it says .51 minutes, so just plug it in

anonymous · Answer

i get about .107 seems reasonable https://www.wolframalpha.com/input/?i=1+%E2%88%92e^-%28.51%2F4.5%29

anonymous · Answer

as long as you get a number between zero and 1 it is a probability, and you would imagine that this one would not be too large because the average is 4.5

anonymous · Answer

yes that is what I got! .107 I wasn't sure but thank you so much for your explanation