Mathematics, 12.02.2020 04:41 germanie123

A restaurant gets an average of 12 phone orders in a 2 hour time period. In order to find the probability that the restaurant will get exactly 2 phone orders in a 30 minute period using the Poisson distribution, what is the average number of phone orders per 30 minutes?

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Answer from: jasontbyrer

The average number of phone calls in a 30 minute period is 3.

The probability to receive exactly 2 calls in that period is 0.224.

Step-by-step explanation:

If we are using the same Poisson distribution in the 2 hour period, then the average of phone orders in a reduced interval will be reduced according to that interval. Since 30 minutes is four times smaller than 2 hours, then the average number of phone orders per 30 minutes is 12 * 1/4 = 3. This can also be computed with a Rule of 3

120 minutes -------------> 12 orders

30 minutes ---------------> X orders

X = 30*12/120 = 3

Lets call Y the amount of phone orders received during a specific (random) 30 minute period. Since the average was 3, then Y has a Poisson distribution with parameter 3. The probability of Y being equal to 2 is

$P(Y=2) = \frac{e^{-3} 3^2 }{2!} = \frac{9}{2} \, e^{-3} = 0.224$

Thus, the probability to receive exactly 2 calls in a 30 minute period is 0.224.

Answer from: Quest

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right

Draw lines to match each expression on the left with the correct product on the right.

Answer from: Quest

{x = -1/2 , y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer: {x = -1/2 , y = -1

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A restaurant gets an average of 12 phone orders in a 2 hour time period. In order to find the probab...

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