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The numbers of accidents which occur on an assembly line each week over a 2 year period are summarised in Table 1. Table 1: Number of accidents, 0 1 2 23456780 3 5 6 8 Frequency 1 HNSKO2I2 14 21 36 18 9 1 (a) Use the data to compute the sample mean number of accidents recorded per area. (b) Suppose the data in Table 1 follows a Poisson distribution. Calculate the theoretical Poisson(A = 3) probabilities for integers in the range 0 to 9 inclusive.

The numbers of accidents which occur on an assembly line each week over a 2 year period are summarised in Table 1. Table 1: Number of accidents, 0 1 2 23456780 3 5 6 8 Frequency 1 HNSKO2I2 14 21 36 18 9 1 (a) Use the data to compute the sample mean number of accidents recorded per area. (b) Suppose the data in Table 1 follows a Poisson distribution. Calculate the theoretical Poisson(A = 3) probabilities for integers in the range 0 to 9 inclusive.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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The numbers of accidents which occur on an assembly line each week over a 2 year period are summarised in Table 1. Table 1: Number of accidents, 2 0 1 2 3 4 5 6 8 Frequency 1 14 21 36 18 9 2 1 2 (a) Use the data to compute the sample mean number of accidents recorded per area. (b) Suppose the data in Table 1 follows a Poisson distribution. Calculate the theoretical Poisson (A = 3) probabilities for integers in the range 0 to 9 inclusive.
Transcribed Image Text:The numbers of accidents which occur on an assembly line each week over a 2 year period are summarised in Table 1. Table 1: Number of accidents, 2 0 1 2 3 4 5 6 8 Frequency 1 14 21 36 18 9 2 1 2 (a) Use the data to compute the sample mean number of accidents recorded per area. (b) Suppose the data in Table 1 follows a Poisson distribution. Calculate the theoretical Poisson (A = 3) probabilities for integers in the range 0 to 9 inclusive.
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(c) Does this Poisson distribution provide a good model for the number of accidents in this example (as per Table 1)? Explain why or why not. Use R to produce a graph to help support your answer (produce the R as part of your answer). [ (d) Use the model in (b) to estimate the probability that less than 2 accidents were recorded in any randomly chosen week. How does this compare to the actual data?
Transcribed Image Text:(c) Does this Poisson distribution provide a good model for the number of accidents in this example (as per Table 1)? Explain why or why not. Use R to produce a graph to help support your answer (produce the R as part of your answer). [ (d) Use the model in (b) to estimate the probability that less than 2 accidents were recorded in any randomly chosen week. How does this compare to the actual data?
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