CAIE S1 2012 June — Question 3

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2012
SessionJune
TopicBinomial Distribution
TypeGeneral probability threshold

3 In Restaurant Bijoux 13\% of customers rated the food as 'poor', 22\% of customers rated the food as 'satisfactory' and \(65 \%\) rated it as 'good'. A random sample of 12 customers who went for a meal at Restaurant Bijoux was taken.
  1. Find the probability that more than 2 and fewer than 12 of them rated the food as 'good'. On a separate occasion, a random sample of \(n\) customers who went for a meal at the restaurant was taken.
  2. Find the smallest value of \(n\) for which the probability that at least 1 person will rate the food as 'poor' is greater than 0.95.