Which of the following distributions can be used to solve the following problem? The average number of cars arriving at a drive-through fast-food restaurant is 3 cars in 10 minutes. What is the probability that exactly four cars will arrive in a 5-minute interval?

You did not state the options to choose from, but I will give a suitable distribution for solving the given problem.

Poisson Distribution

Step-by-step explanation:

Poisson Distributions are used in calculating the probability of an event occurring over a given interval.

It is calculated using the formula

P(X = x) = [e^(-β)β^x]/x!

Where e = 2.718

β = mean or expected value of the variable.

x = number of successes of the event

Applying this to the given problem, suppose we are trying to find the probability that exactly four cars will arrive in 5 minute interval.

Average number of cars arriving = 3/10 = 0.3

The probability of success over a short interval must be the same probability over a long interval, so we have β = 0.3 × 5 = 1.5

x = 4

P(X = 4) = [e^(-1.5) (1.5)^(4)]/4!

= 0.047066518

≈ 0.0047

There is a 0.47% chance that exactly four cars will arrive in 5 minute interval.

x = 45

y = 60

z = 75

Step-by-step explanation:

We can create three different equations with the given variables:

x + y + z = 180

y + z = 3 x

z = y + 15

then we can use this last equation to substitute for 'z" in the second equation:

y + z = 3x

y + y + 15 = 3 x

2 y + 15 = 3 x

x = 2/3 y + 5

Then we can re-write the first equation in terms of y and solve for this unknown:

2/3 y + 5 + y + y + 15 = 180

2/3 y + 2 y = 160

8/3 y = 160

y = 3 * 160 /8

y = 60

Then   x = 2/3 (60) + 5 = 45

so x = 45

and finally:   z = 60 + 15 = 75

so  z = 75