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 &amp; 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&gt;800 is 1, &gt;950 is close to 0.95, &gt;1000 is close to 0.5 &amp; so on.
I am not sure if these probabilities are  correct esp. for high order counts, e.g. for &gt;1050 orders prob is less than 0.1, for &gt;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(&quot;Orders Count&quot;)
plt.ylabel(&quot;Probability&quot;)
plt.title(&quot;Probabilities of Minimum Orders Count&quot;); 


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

Problem is low probability of getting orders &gt;=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 $31.6$.

At such values, the Poisson law pretty much behaves like a normal distribution, so the probability of getting a value greater than 1100 would be very close to 0 (around 0.1%).

Perhaps what you need is not a Poisson law, but a truncated normal distribution?