The problem is asking for the probability that a clothing store will have more than 12 customers in the first hour, given that on average, the store gets 120 customers per day and is open for 12 hours each day. First, we need to find the average number of customers per hour. Since the store is open for 12 hours each day and gets 120 customers per day, the average number of customers per hour is 120/12 = 10 customers. The problem states that the number of customers follows a Poisson distribution. The Poisson distribution gives the probability of a given number of events (in this case, customers) occurring in a fixed interval of time (in this case, an hour) if these events occur with a known average rate (in this case, 10 customers per hour) and independently of the time since the last event. The probability mass function of a Poisson distribution is given by: P(X=k) = λ^k * e^-λ / k! where λ is the average rate of occurrence (10 customers per hour), k is the actual number of occurrences (the number of customers), e is the base of the natural logarithm (approximately 2.71828), and k! is the factorial of k. We want to find the probability that the store will have more than 12 customers in the first hour, i.e., P(X12). This is equal to 1 - P(X

Question

The problem is asking for the probability that a clothing store will have more than 12 customers in the first hour, given that on average, the store gets 120 customers per day and is open for 12 hours each day. First, we need to find the average number of customers per hour. Since the store is open for 12 hours each day and gets 120 customers per day, the average number of customers per hour is 120/12 = 10 customers. The problem states that the number of customers follows a Poisson distribution. The Poisson distribution gives the probability of a given number of events (in this case, customers) occurring in a fixed interval of time (in this case, an hour) if these events occur with a known average rate (in this case, 10 customers per hour) and independently of the time since the last event. The probability mass function of a Poisson distribution is given by: P(X=k) = λ^k * e^-λ / k! where λ is the average rate of occurrence (10 customers per hour), k is the actual number of occurrences (the number of customers), e is the base of the natural logarithm (approximately 2.71828), and k! is the factorial of k. We want to find the probability that the store will have more than 12 customers in the first hour, i.e., P(X>12). This is equal to 1 - P(X<=12), because the total probability must be 1. To find P(X<=12), we sum up the probabilities P(X=k) for k=0 to 12. P(X<=12) = Σ P(X=k) for k=0 to 12 = Σ [λ^k * e^-λ / k!] for k=0 to 12 = Σ [10^k * e^-10 / k!] for k=0 to 12 We can calculate this sum using a calculator or a software that can handle statistical calculations. Finally, we subtract this sum from 1 to get P(X>12). P(X>12) = 1 - P(X<=12) Without the actual calculations, we can't determine which of the given options a, b, or c is the correct answer. However, this is the process you would follow to solve this problem.

Knowee AI · Accepted Answer

The problem is asking for the probability that a clothing store will have more than 12 customers in the first hour, given that on average, the store gets 120 customers per day and is open for 12 hours each day. First, we need to find the average number of customers per hour. Since the store is open for 12 hours each day and gets 120 customers per day, the average number of customers per hour is 120/12 = 10 customers. The problem states that the number of customers follows a Poisson distribution. The Poisson distribution gives the probability of a given number of events (in this case, customers) occurring in a fixed interval of time (in this case, an hour) if these events occur with a known average rate (in this case, 10 customers per hour) and independently of the time since the last event. The probability mass function of a Poisson distribution is given by: P(X=k) = λ^k * e^-λ / k! where λ is the average rate of occurrence (10 customers per hour), k is the actual number of occurrences (the number of customers), e is the base of the natural logarithm (approximately 2.71828), and k! is the factorial of k. We want to find the probability that the store will have more than 12 customers in the first hour, i.e., P(X>12). This is equal to 1 - P(X<=12), because the total probability must be 1. To find P(X<=12), we sum up the probabilities P(X=k) for k=0 to 12. P(X<=12) = Σ P(X=k) for k=0 to 12 = Σ [λ^k * e^-λ / k!] for k=0 to 12 = Σ [10^k * e^-10 / k!] for k=0 to 12 We can calculate this sum using a calculator or a software that can handle statistical calculations. Finally, we subtract this sum from 1 to get P(X>12). P(X>12) = 1 - P(X<=12) Without the actual calculations, we can't determine which of the given options a, b, or c is the correct answer. However, this is the process you would follow to solve this problem.

On an average, a clothing store gets 120 customers per day. Let the random variable X~P (120). What is the probability that the store will have more than 12 customers in the first hour? "Assume the store is open 12 hours each day."Question 5Answera.0.05b.0.0010c.0.2084

Question

Solution

Similar Questions

Upgrade your grade with Knowee