Tim Gan Math
Sign up free

Distribution of defective items

Distribution of defective items

IB Year 5 | Grade 11

The probability that a pen drawn at random from a box of pens is defective is \(0.5\). If a sample of \(7\) pens is taken, find the probability that it will contain

  1. no defective pens;
  2. \(5\) or \(6\) defective pens;
  3. less than \(3\) defective pens;
  4. the most likely number of defective pens in the sample of \(7\) pens;
  5. the expected number of defective pens in the sample and their standard deviation.

Solution:

Solution locked

680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.

Create free accountSign inIB Math tuition

Create a free account to practise similar questions.

Create free accountSign inIB Math tuition
Answer:Assuming independent sampling: (a) \(\dfrac1{128}\approx0.00781\). (b) \(\dfrac7{32}\approx0.219\). (c) \(\dfrac{29}{128}\approx0.227\). (d) \(3\) and \(4\). (e) expectation \(3.5\), standard deviation \(\dfrac{\sqrt7}{2}\approx1.32\).

Need help? Join our JC Math tuition classes.

Learn more