Two part question please answer both parts and show all work

Two part question, please answer both parts and show all work to justify final answer. Thank you.

Your store has, on average, 40 customers per hour.

What is the probability your next customer will enter in the next minute?

What is the probability you will not get a customer in the next five minutes?

Solution

a)

There are 40 customers an hour (60 min), so there are 40/60 = 0.6666667 customers a minute, on average.

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    0.666666667      
          
x = the number of successes =    1      
          
Thus, the probability is          
          
P (    1   ) =    0.342278079

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b)

There are 40 customers an hour (60 min), so there are 40/60 = 0.6666667 customers a minute, on average.

Hence, in 5 minutes, an average of 0.6666667*5 = 3.33333333.

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    3.333333333      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.035673993 [ANSWER]