CAIE S1 2010 November — Question 7

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2010
SessionNovember
TopicNormal Distribution
TypeFind p then binomial probability

7 The times spent by people visiting a certain dentist are independent and normally distributed with a mean of 8.2 minutes. \(79 \%\) of people who visit this dentist have visits lasting less than 10 minutes.
  1. Find the standard deviation of the times spent by people visiting this dentist.
  2. Find the probability that the time spent visiting this dentist by a randomly chosen person deviates from the mean by more than 1 minute.
  3. Find the probability that, of 6 randomly chosen people, more than 2 have visits lasting longer than 10 minutes.
  4. Find the probability that, of 35 randomly chosen people, fewer than 16 have visits lasting less than 8.2 minutes. \footnotetext{Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. }