Answer:
The probability that a randomly selected call time will be less than 30 seconds is 0.7443.
Step-by-step explanation:
We are given that the caller times at a customer service center has an exponential distribution with an average of 22 seconds.
Let X = caller times at a customer service center
The probability distribution (pdf) of the exponential distribution is given by;
Here, = exponential parameter
Now, the mean of the exponential distribution is given by;
Mean =
So, ⇒
SO, X ~ Exp()
To find the given probability we will use cumulative distribution function (cdf) of the exponential distribution, i.e;
; x > 0
Now, the probability that a randomly selected call time will be less than 30 seconds is given by = P(X < 30 seconds)
P(X < 30) =
= 1 - 0.2557
= 0.7443
Answer:
-72 i notice you're having trouble message me and ill help you
if you know the tables then you can do that easily.
Graph it and out the letters on where the dot ends up on the graph. I cant show you because i cant do a graph on here
With this problem, we have two right triangles meaning we will end up using the Pythagorean Theorem. For the sake of the problem, let's say the boat is at point D. The two triangles we have are ΔACD and ΔABD. Let's first go through and define the lines.
Let's start with ΔACD:
Port A is 24 miles from Port C so AC = 24mi. We will represent this as line a
Port C is 25 miles from Boat D so CD (the hypotenuse) = 25mi. We will represent this as line c
We do not know the distance between Port A and Boat D (AD also known as line b) so let's calculate that since we will need it at the end.
We can calculate line b's length using the theorem: a² + b² = c²
a = 24mi
b = ?
c = 25mi
So
(24)² + b² = (25)²
576 + b² = 625
Subtract 576 from both sides to isolate b²
576 + b² - 576 = 625 - 576
b² = 49
Now take the square root of both sides
√b² = √49
b = 7 miles.
Now we know that the distance between Port A and Boat D is 7 miles.
Now let's move on to ΔABD
Port B is 15 miles from Port A so AB = 15mi. We will represent this as line a
Boat D is 7 miles from Port A so AD = 7mi. This will still be line b
We do not know the distance between Port B and Boat D (BD also known as line c).
Time to use the Pythagorean Theorem once more!
a² + b² = c²
15² + 7² = c²
225 + 49 = c²
274 = c²
Take the square root of both sides
√274 = √c²
c ≈ 16.6mi when we round to the nearest tenth
So the distance between Port B and the boat is 16.6 miles