6 The mean Intelligence Quotient (IQ) of a random sample of 15 pupils at \(\operatorname { School } A\) is 109 . The mean IQ of a random sample of 20 pupils at School \(B\) is 112 . You may assume that the IQs for the populations from which these samples are taken are normally distributed, and that both distributions have standard deviation 15. Find a \(90 \%\) confidence interval for \(\mu _ { B } - \mu _ { A }\), where \(\mu _ { A }\) and \(\mu _ { B }\) are the population mean IQs.