The coffee company American Expresso has a promotion where "if you don't get your take away coffee within 180 seconds, it's free!".
American Expresso has commissioned an independent study which found that the time to prepare a take away coffee at one of their stores is approximately normally distributed with a mean time of 156 seconds and a standard deviation of 24 seconds.
You may find this standard normal table useful throughout the following questions.
a)Calculate the percentage of take away coffees that are given to customers for free according to the promotion. Give your answer as a percentage to 1 decimal place.
Percentage of free coffees = ? %
b)Some shareholders are unhappy with the terms of the promotion and suggest that the time limit should be such that at most only 2.5% of take away coffees are given for free under the promotion.
Calculate the time limit such that this requirement is satisfied. Give your answer as a whole number.
Time limit = ? seconds