# Probabilities of a Poisson distribution not making sense

I am trying to find probabilities of orders a restaurant gets on Sunday's. For last 6 months average orders are 1000 without any big anomalies like 700 or 1300. This is a case of poisson distribution & I used scipy library in python and plotted the probabilities.

The graph shows probabilities that of getting orders greater than values on x-axis, e.g. probability of orders>800 is 1, >950 is close to 0.95, >1000 is close to 0.5 & so on.

I am not sure if these probabilities are correct esp. for high order counts, e.g. for >1050 orders prob is less than 0.1, for >1100 almost zero which I find odd because its quite likely to have 1100 or little more orders occasionally. So what are thoughts on probabilities calculated using Poisson distribution.

prob_arr=[]
orders_arr=[]

dist=poisson(1000) #mu=1000

for num_orders in range(800,1201,50):
prob_arr.append(dist.sf(num_orders)) #survival function
orders_arr.append(num_orders)

plt.figure(figsize=(12,4))
plt.plot(orders_arr,prob_arr,linewidth=2)
plt.xlabel("Orders Count")
plt.ylabel("Probability")
plt.title("Probabilities of Minimum Orders Count");


As suggested by @Romain Reboulleau tried truncated norm distribution and below graph shows probabilities of getting orders >than values on x-axis derived using scipy truncnorm.

Problem is low probability of getting orders >=1100, it is 1.3% as per truncnorm vs only 0.09% with poisson. This would make non-stats business managers laugh and I am not sure how to justify this.

This seems quite right to me. A poisson(1000) law has a standard deviation of $$\sqrt{1000}$$ which is something around $$31.6$$.