1. The Tourism Board found that sixty two percent of airline passengers travelled overseas from a particular airport. If a random sample of 500 passengers is selected, what is the approximate probability that at least 290 passengers are actually travelled overseas? (Use the normal approximation).
2. The Chemical Manufacturing Association reports that companies producing industrial chemicals lost 10.1 days of work due to injury or illness for each 10,000 worker-hours of production during 2014. What is the probability that a typical company in this industry would experience no more than 8 days lost over the next 10,000 worker-hours of production? (Use the normal approximation of the Poisson distribution).
3. A marketing company is conducting an experiment in which customers have to taste one of two different brands of soft drink. It is found that 46% of the customers are able to correctly identify the brand tasted. If a random sample of 90 customers is taken, what is the probability that the sample will have between 45% and 55% of the identifications correct?