The number of parking tickets issued in a certain city on any given weekday has a Poisson distribution with parameter = 50. (a)Calculate the approximate probability that between 35 and 70 tickets are given out on a particular day.

(b)Calculate the approximate probability that the total number of tickets given out during a 5-day week is between 225 and 275.

(c)Use software to obtain the exact probabilities in (a) and (b) and compare to their approximations.

Explanation:

(a) Calculate the approximate probability that between 35 and 70 tickets are given out on a particular day.

(using continuity correction)

= 0.9981 - 0.0143 (using standard normal tables)

= 0.9839

b) Consider is the random variable that represents the number of parking tickets issued in certain city in a 5-day week

The mean number of parking ticket issued in a particular city on 5-day week is

Therefore, the required probability is

= 0.9463 - 0.0537 (using standard normal tables)

= 0.8926

c) see the attached file  

image 1 (the approximate probability of part a )

image 2 (the approximate probability of part b )

From the two graph observed that the probability obtained using software is approximately same as calculated by manually

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