Mathematics

1. 1.

   X follows a binomial distribution with n = 10 and p = 0.3. Calculate P(X >= 3).

   [3 marks]
2. 2.

   The heights of adult men are modelled by a normal distribution with mean 170 cm and standard deviation 8 cm. Calculate the probability that a randomly chosen man is taller than 182 cm.

   [3 marks]
3. 3.

   For events A and B, P(A) = 0.6, P(B) = 0.5 and P(A and B) = 0.35. Find P(A | B), determine whether A and B are independent, and find P(A or B).

   [4 marks] · no calculator
4. 4.

   A coin is tossed 20 times and lands heads 15 times. Test, at the 5% significance level, whether the coin is biased towards heads. State your hypotheses and conclusion.

   [4 marks]
5. 5.

   A machine fills bottles with mean volume 250 ml and known standard deviation 6 ml. A sample of 36 bottles has mean 247.8 ml. Test at the 5% level whether the mean volume has decreased.

   [5 marks]
6. 6.

   For 8 pairs of data (x, y) with x between 2 and 9: sum x = 40, sum y = 96, Sxx = 60, Sxy = 84, Syy = 120. Find the regression line of y on x, predict y when x = 7, find the product moment correlation coefficient, and interpret the gradient.

   [6 marks]

Original, unofficial practice questions from SubjectScout — not official past-paper questions.