A computer program randomly selects one of the digits 0 to 9 each time it is run. Each digit is equally likely to be selected. The program is run 8 times.
Find the probability that the program selects the digit 7 exactly 2 times.
Find the probability that the program selects the digit 7 more than 3 times.
Priya believes that the program does not select the digits equally often and that the probability of selecting a 7 is greater than 110\displaystyle \frac{1}{10}101. To test this claim, she runs the program 40 times and it selects a 7 on 8 occasions. Stating your hypotheses clearly, test Priya's claim at the 5% significance level.
33 exam-style questions on Edexcel AS Level Maths Hypothesis Testing, covering 7.1 Hypothesis Testing, 7.2 Finding Critical Values, 7.3 One-Tailed Tests, and 7.4 Two-Tailed Tests. Each one has a worked solution and a mark scheme showing where the marks go.