The time between calls to a plumbing supply business is exponentially distributed with a mean time between calls of 13 minutes. (a) What is the probability that there are no calls within a 30-minute interval

P(X>30) = 1 - F(30) = 0.0995

Step-by-step explanation:

Let X be the exponential distributed random variable of time between the calls with the given mean of 13 minutes

E(X) = 13

As we have the continuous random variable (time), the distribution is

F(x) = 1 - e^(-λx)

Now we need to calculate the λ from the formula of exponential distribution which is

E(X) = 1/λ = 15

So, λ = 1/15

Now, we will calculate the probability that there are no call within 30 minutes time interval, It mean we need to find the probability when time is greater than 30 (X>30)

P (X>30) = 1 - F(30) = 1 - (1 - e^(-30*1/13)

P (X>30) = e^(-30/13) = e^(-2.3) = 0.0995

P(X>30) = 0.0995

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560