OCR S3 2012 June — Question 1

Exam BoardOCR
ModuleS3 (Statistics 3)
Year2012
SessionJune
TopicLinear combinations of normal random variables
TypeConfidence interval for single proportion

1 A machine fills packets of flour whose nominal weights are 500 g . Each of a random sample of 100 packets was weighed and 14 packets weighed less than 500 g . The population proportion of packets that weigh less than 500 g is denoted by \(p\).
  1. Calculate an approximate \(95 \%\) confidence interval for \(p\).
  2. The weights of the packets, in grams, are normally distributed with mean \(\mu\) and variance 50 . Assuming that \(p = 0.14\), calculate the value of \(\mu\).