4. The journey time for Charlie to travel to the train station is normally distributed with...

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4. The journey time for Charlie to travel to the train station is normally distributed with mean 25 miutes and standard deviation 6 mimutes. If Charlie's journey time is less than 20 minutes, he will have time to buy a coffee before boarding his train (a) Find the probability that, on a randomly selected day, Charlie has time to buy a coffee. (3) In a particular week, Charlie travels to the station on 2 days. (b) Find the probability that be has time to buy a coffee on just one of these days. (3) On 1% of days, Charlie's journey time is longer than m minutes. (c) Find the value of m. (3) A new road is built and this should make Charlie's joumey time to the station more reliable. (d) State, giving a reason. what effect you would expect this to have on the standard (1) After the new road was built, Charlie's journey time to the station is still modelled by a nomal distribution with mean 25 minutes but the standard deviation, o, has changed In the first 20 journeys to the station using this new road, Charlie took longer than 30 minutes on 3 occasions. (e) Estimate the value of o. (4) 4. The journey time for Charlie to travel to the train station is normally distributed with mean 25 miutes and standard deviation 6 mimutes. If Charlie's journey time is less than 20 minutes, he will have time to buy a coffee before boarding his train (a) Find the probability that, on a randomly selected day, Charlie has time to buy a coffee. (3) In a particular week, Charlie travels to the station on 2 days. (b) Find the probability that be has time to buy a coffee on just one of these days. (3) On 1% of days, Charlie's journey time is longer than m minutes. (c) Find the value of m. (3) A new road is built and this should make Charlie's joumey time to the station more reliable. (d) State, giving a reason. what effect you would expect this to have on the standard (1) After the new road was built, Charlie's journey time to the station is still modelled by a nomal distribution with mean 25 minutes but the standard deviation, o, has changed In the first 20 journeys to the station using this new road, Charlie took longer than 30 minutes on 3 occasions. (e) Estimate the value of o. (4)

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Let X Jourmey time Normal2562 X 20 20 256 08333 1 08333 02023 where x cdf of standar d ... View the full answer