An automatic car wash takes exactly 5 minutes to wash a car. On average, 10 cars per hour arrive at the car wash. Suppose that, 30 minutes before closing time, five cars are in line. If the number of cars in any time interval follows a Poisson distribution, and if the car was is in continuous operation until closing time, what is the probability that anyone will be in line at closing time

0.9595724

Step-by-step explanation:

Time taken to wash a car (μ) = 5 minutes

Hence, Number of cars washed per hour = 60/5 = 12 cars

If 5 cars arrive, 30 minutes to closing ; it takes 25 minutes to finish up ;

If 1 more car arrives, then it takes exactly 30 minutes

Hence, there will be no one in line at closing ;

IF 0 or 1 car arrives, if more than 1 car arrives, then there will be people in line at closing.

Hence, probability of waiting in line at closing :

1 - [p(0) + p(1)]

Using poisson :

P(x) = [(e^-μ) * (μ^x)] / x!

If x = 0

P(0) = [(e^-5) * (5^0)] / 0!

P(0) = (0.0067379 * 1) / 1

P(0) = 0.0067379

X = 1

P(1) = [(e^-5) * (5^1)] / 1!

P(0) = (0.0067379 * 5) / 1

P(0) = 0.0336897

Hence,

1 - (0.0067379 + 0.0336897)

1 - 0.0404276

= 0.9595724

Hence, the probability that anyone would be in the car washing line after closing is 0.9595724

step-by-step explanation:

given expression is .

now we need to simplify the given expression .

we know that square root is equivalent to the power 1/2. so that means we can take half of the exponents to get the square root of given expression.

expanding that will give a very very large number so let's keep answer in exponent form.

a mantle plume is an upwelling of abnormally hot rock within the earth's mantle. as the heads of mantle plumes can partly melt when they reach shallow depths, they are thought to be the cause of volcanic centers known as hotspots and probably also to have caused flood basalts.

step-by-step explanation: