The number of parking tickets issued in a certain city on any given weekday has a Poisson distribution with parameter μ = 48. a) Calculate the approximate probability that between 31 and 72 tickets are given out on a particular day. (using the normal approximation. For this, you need to use a continuity correction, so find the probability between 31 -0.5 and 72 +0.5) b) Calculate the approximate probability that the total number of tickets given out during a 5-day week is between 230 and 260. (using the normal approximation. Note: For this question you are find a probability for a Total for 5 days...so use the mean and standard deviation for Totals. Also the continuity correction requires you to find the probability the total is between 230 - 0.5 and 260 + 0.5)) c) Use software to obtain the exact probabilities in (a) and (b) and compare. (use the Poisson distribution) P (31 ≤ x ≤72) = = P (230 ≤X ≤260) = =

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The number of parking tickets issued in a certain city on any given weekday has a Poisson
distribution with parameter μ = 48.
a) Calculate the approximate probability that between 31 and 72 tickets are given out on a
particular day.
(using the normal approximation. For this, you need to use a continuity correction, so find the
probability between 31 -0.5 and 72 +0.5)
b) Calculate the approximate probability that the total number of tickets given out during a 5-day
week is between 230 and 260.
(using the normal approximation. Note: For this question you are find a probability for a Total for 5
days...so use the mean and standard deviation for Totals. Also the continuity correction requires
you to find the probability the total is between 230 - 0.5 and 260 + 0.5))
c) Use software to obtain the exact probabilities in (a) and (b) and compare. (use the Poisson
distribution)
P (31 ≤X ≤72)
=
P (230 ≤X ≤260) =
=
Transcribed Image Text:The number of parking tickets issued in a certain city on any given weekday has a Poisson distribution with parameter μ = 48. a) Calculate the approximate probability that between 31 and 72 tickets are given out on a particular day. (using the normal approximation. For this, you need to use a continuity correction, so find the probability between 31 -0.5 and 72 +0.5) b) Calculate the approximate probability that the total number of tickets given out during a 5-day week is between 230 and 260. (using the normal approximation. Note: For this question you are find a probability for a Total for 5 days...so use the mean and standard deviation for Totals. Also the continuity correction requires you to find the probability the total is between 230 - 0.5 and 260 + 0.5)) c) Use software to obtain the exact probabilities in (a) and (b) and compare. (use the Poisson distribution) P (31 ≤X ≤72) = P (230 ≤X ≤260) = =
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