This problem can be solved using the Poisson distribution formula. The Poisson distribution gives the probability of a given number of events (in this case, customers arriving at a restaurant) happening in a fixed interval of time (120 minutes in this case) when these events occur with a known average rate (9 customers per hour) and independently of the time since the last event.

The formula for the Poisson distribution is:

P(x; μ) = (e^-μ) * (μ^x) / x!

where:
- P(x; μ) is the probability of x events in an interval,
- e is the base of the natural logarithm (approximately equal to 2.71828),
- μ is the average rate of value (mean value),
- x is the actual number of successes that result from the experiment.

In this case, we want to find the probability (P) that exactly 6 customers (x) arrive in a 120 minute period. The rate is 9 customers per hour, so in 120 minutes (or 2 hours), the average rate (μ) is 9 customers/hour * 2 hours = 18 customers.

Substituting these values into the formula, we get:

P(6; 18) = (e^-18) * (18^6) / 6!

Calculating this gives a result of approximately 0.0437, so the correct answer is c. 0.0437.

Question

This problem can be solved using the Poisson distribution formula. The Poisson distribution gives the probability of a given number of events (in this case, customers arriving at a restaurant) happening in a fixed interval of time (120 minutes in this case) when these events occur with a known average rate (9 customers per hour) and independently of the time since the last event.

The formula for the Poisson distribution is:

P(x; μ) = (e^-μ) * (μ^x) / x!

where:
- P(x; μ) is the probability of x events in an interval,
- e is the base of the natural logarithm (approximately equal to 2.71828),
- μ is the average rate of value (mean value),
- x is the actual number of successes that result from the experiment.

In this case, we want to find the probability (P) that exactly 6 customers (x) arrive in a 120 minute period. The rate is 9 customers per hour, so in 120 minutes (or 2 hours), the average rate (μ) is 9 customers/hour * 2 hours = 18 customers.

Substituting these values into the formula, we get:

P(6; 18) = (e^-18) * (18^6) / 6!

Calculating this gives a result of approximately 0.0437, so the correct answer is c. 0.0437.

Knowee AI · Accepted Answer

This problem can be solved using the Poisson distribution formula. The Poisson distribution gives the probability of a given number of events (in this case, customers arriving at a restaurant) happening in a fixed interval of time (120 minutes in this case) when these events occur with a known average rate (9 customers per hour) and independently of the time since the last event.

The formula for the Poisson distribution is:

P(x; μ) = (e^-μ) * (μ^x) / x!

where:
- P(x; μ) is the probability of x events in an interval,
- e is the base of the natural logarithm (approximately equal to 2.71828),
- μ is the average rate of value (mean value),
- x is the actual number of successes that result from the experiment.

In this case, we want to find the probability (P) that exactly 6 customers (x) arrive in a 120 minute period. The rate is 9 customers per hour, so in 120 minutes (or 2 hours), the average rate (μ) is 9 customers/hour * 2 hours = 18 customers.

Substituting these values into the formula, we get:

P(6; 18) = (e^-18) * (18^6) / 6!

Calculating this gives a result of approximately 0.0437, so the correct answer is c. 0.0437.

Customers arrive at a restaurant at a random rate of 9 per hour. What the probability that during any 120 minute period, the number of customers arriving at the restaurant is exactly 6.Question 22Select one:a.0.1171b.0.0255c.0.0437d.0.0025

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