The coffee company American Expresso has a new promotion where "if you don't get your take away coffee within 180 seconds, it's free!". However, far too many coffees seem to have been given away since the promotion began.
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 209 seconds and a standard deviation of 21 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)Shareholders are extremely 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