Final answer:
To calculate the probabilities of the given scenarios, you can use the Poisson distribution formula and the Central Limit Theorem. Approximations can be made for large values of the parameter, but exact probabilities can be obtained using software.
Step-by-step explanation:
To calculate the approximate probability that between 35 and 70 tickets are given out on a particular day, we can use the Poisson distribution formula. The probability is equal to the sum of the probabilities of each individual outcome within the range. In this case, we would need to calculate P(35), P(36), P(37), ..., P(70) and then sum them up.
To calculate the approximate probability that the total number of tickets given out during a 5-day week is between 225 and 275, we can use the Central Limit Theorem. The Poisson distribution can be approximated by a normal distribution when the parameter m is large enough. We can calculate the mean and standard deviation of the distribution and use the cumulative distribution function to find the probability of the range.
To obtain the exact probabilities in (a) and (b), you can use software like Excel or statistical calculators that have built-in functions for the Poisson distribution and the normal distribution. These tools can provide more accurate results than the approximations.