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# AS Further Stats. Poisson Distribution- Bionamial approximation watch

1. How do I solve these questions?
6 Betty Drives along a 50 mile stretch of motorway 5 days a week 50 weeks a year. She takes no notice the 70 mph speed limit, when the traffic allows, travels between 95 and 105 mph. From time to time she is caught by the police and fined, but she estimates the probability of this happening on and day is 1/300. If she gets caught three times within three years she will be disqualified from driving. Use Betty's estimates Of probability to answer the following questions.

i. What is the probability of her being caught exactly once in any year?
ii. What is the probability of her being caught less than three times in three years?
iii. What is the probability of her being caught exactly three times in three years?

Betty is in fact caught one day and decides to be somewhat cautious, reducing her normal speed to between 85 and 95 mph. She believes this will reduce the probability of her being caught to 1/500

iv What is the probability that she is caught less than twice in the next three years?
2. (Original post by EBris.)
How do I solve these questions?
6 Betty Drives along a 50 mile stretch of motorway 5 days a week 50 weeks a year. She takes no notice the 70 mph speed limit, when the traffic allows, travels between 95 and 105 mph. From time to time she is caught by the police and fined, but she estimates the probability of this happening on and day is 1/300. If she gets caught three times within three years she will be disqualified from driving. Use Betty's estimates Of probability to answer the following questions.

i. What is the probability of her being caught exactly once in any year?
ii. What is the probability of her being caught less than three times in three years?
iii. What is the probability of her being caught exactly three times in three years?

Betty is in fact caught one day and decides to be somewhat cautious, reducing her normal speed to between 85 and 95 mph. She believes this will reduce the probability of her being caught to 1/500

iv What is the probability that she is caught less than twice in the next three years?
Each part can be worked out using binomial distribution, but the number of days she travels is large enough (with probability of getting caught being small enough) to approximate each one using Poisson distribution.

For example;

(i) The catching can be binomially distributed by where is the amount of days she travels along this motorway over a single year (so, work out what that is). Then the mean of this is therefore the distribution can be approximated by and so use this to determine

Repeat similarly for others.

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Updated: February 10, 2018
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