Final answer:
The question pertains to using the Poisson distribution to calculate the probability of at least 7 customers entering a bakery in a 6-minute interval, given a Poisson process with a rate of 30 customers per hour.
Step-by-step explanation:
The subject of the question is probability theory, a branch of mathematics focused on the analysis of random variables and events. The student is being asked to calculate the probability that at least 7 customers will enter a bakery between 11:30 am and 11:36 am, given that customers arrive according to a Poisson process. Since we expect 30 customers to arrive per hour and the time between arrivals is exponentially distributed, we find that on average there is one customer every two minutes. To find the required probability, we can use the Poisson distribution formula, which for a time interval of 6 minutes (since we want to know the probability for the time period between 11:30 am and 11:36 am) with a rate of 3 customers per 6 minutes (since 30 customers arrive per hour and we are looking at a 1/10 of that hour), we have λ = 3 for 6 minutes. The probability of at least 7 customers arriving is the sum of the probabilities of exactly 7 customers arriving, 8 customers, 9, and so on. However, due to the complexity of calculating the sum of probabilities for 7 or more arrivals, which involves multiple uses of the Poisson probability mass function (PMF), it may be easier to calculate 1 minus the probability of 6 or fewer arrivals.