Answer :
When considering the number of customers who buy a sub at Jersey Mike's sandwich shop in a 30-minute time frame, it is important to choose a distribution that appropriately models the count of events happening within a fixed interval of time. Let's analyze the given options:
1. Hypergeometric Distribution: This distribution models the number of successes in a sequence of draws from a finite population without replacement. Since the number of customers is not being drawn from a finite population in a specific sequence, this distribution is not appropriate.
2. Continuous Distribution: Continuous distributions are used to model data that can take any value within a given range. The number of customers is a discrete count and not a continuous variable, so this distribution does not fit.
3. Binomial Distribution: The binomial distribution is used to model the number of successes in a fixed number of independent Bernoulli trials, with a constant probability of success in each trial. However, customer arrivals are not a fixed number of trials; they are more naturally represented as a potentially infinite number of opportunities within a given time frame.
4. Poisson Distribution: This distribution is used to model the number of events occurring in a fixed interval of time or space, assuming the events happen with a constant mean rate and independently of the time since the last event. This is particularly suitable for modeling the number of customers arriving, as it accounts for random and independent arrivals within a fixed period.
The number of customers buying a sub at Jersey Mike's sandwich shop is likely to be described by a Poisson distribution. This distribution accurately reflects the nature of the event count over a specified period with a constant rate of customer arrivals.
Therefore, the correct answer is:
- Poisson distribution.
1. Hypergeometric Distribution: This distribution models the number of successes in a sequence of draws from a finite population without replacement. Since the number of customers is not being drawn from a finite population in a specific sequence, this distribution is not appropriate.
2. Continuous Distribution: Continuous distributions are used to model data that can take any value within a given range. The number of customers is a discrete count and not a continuous variable, so this distribution does not fit.
3. Binomial Distribution: The binomial distribution is used to model the number of successes in a fixed number of independent Bernoulli trials, with a constant probability of success in each trial. However, customer arrivals are not a fixed number of trials; they are more naturally represented as a potentially infinite number of opportunities within a given time frame.
4. Poisson Distribution: This distribution is used to model the number of events occurring in a fixed interval of time or space, assuming the events happen with a constant mean rate and independently of the time since the last event. This is particularly suitable for modeling the number of customers arriving, as it accounts for random and independent arrivals within a fixed period.
The number of customers buying a sub at Jersey Mike's sandwich shop is likely to be described by a Poisson distribution. This distribution accurately reflects the nature of the event count over a specified period with a constant rate of customer arrivals.
Therefore, the correct answer is:
- Poisson distribution.
