CAIE S1 2014 June — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2014
SessionJune
TopicNormal Distribution
TypeDirect binomial from normal probability

5 When Moses makes a phone call, the amount of time that the call takes has a normal distribution with mean 6.5 minutes and standard deviation 1.76 minutes.
  1. \(90 \%\) of Moses's phone calls take longer than \(t\) minutes. Find the value of \(t\).
  2. Find the probability that, in a random sample of 9 phone calls made by Moses, more than 7 take a time which is within 1 standard deviation of the mean.