Question: An extensive survey carried out by the Automobile Drivers Association (ADA) on behalf of the Ministry of Transport revealed that 70% of the car owners were in favour of a decrease in the speed limit on the major highways of the country.

1. A sample of fifteen car owners is randomly selected. What is the probability that more than ten are in favour of a decrease in the speed limit?
   (we compute this using Excel’s function Binomdist).
2. If a sample of ten car drivers were randomly selected what is the probability that more than five but fewer than nine will be in favour of a decrease in the speed limit?
3. If a sample of 1,200 car drivers were randomly selected what is the probability that fewer than 840 will be in favour of a decrease in the speed limit?
4. Assume now that the results obtained by ADA were based on a random sample of 2,500 car drivers. Assume furthermore that this sample indicated that 1,750 car drivers were in favour of a decrease in the speed limit. Find the 95% confidence limits of the proportion of car drivers who favour a decrease in the speed limit.

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