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

step-by-step explanation:

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.