Probability, Probability Distributions and Regression · CAPE Integrated Mathematics

14 past-paper questions on Probability, Probability Distributions and Regression, part of Statistics, from every CAPE Integrated Mathematics paper on Quelpr.

1. 3(d)(i)3 marks· CAPE Integrated Mathematics · 2016 · Paper 2Show that a = 3.
2. 3(d)(ii)3 marks· CAPE Integrated Mathematics · 2016 · Paper 2Find the variance, Var(X).
3. 4(c)(i)2 marks· CAPE Integrated Mathematics · 2016 · Paper 2Given that X ~ Bin(n, 0.4) where the mean is 3.2, show that the number of trials, n = 8.
4. 4(c)(ii)4 marks· CAPE Integrated Mathematics · 2016 · Paper 2Find P(X >= 6).
5. 4(d)(i)2 marks· CAPE Integrated Mathematics · 2016 · Paper 2The mass of barrels arriving in a specific country follows a normal distribution with mean 140 kg and standard deviation 5 kg. Show that the z-value of a barrel of mass 132 kg is z = -1.6.
6. 4(d)(ii)4 marks· CAPE Integrated Mathematics · 2016 · Paper 2Find the probability that a barrel selected at random weighs more than 132 kg.
7. 3(c)5 marks· CAPE Integrated Mathematics · 2017 · Paper 2A student is selected at random from the 50 students in the sample. Using the histogram or otherwise, determine the probability that the student spends 26 minutes or less than 26 minutes reading.
8. 3(d)(i)2 marks· CAPE Integrated Mathematics · 2017 · Paper 2Determine the value of q in the probability distribution table.
9. 3(d)(ii)5 marks· CAPE Integrated Mathematics · 2017 · Paper 2Complete the probability distribution table.
10. 3(d)(iii)5 marks· CAPE Integrated Mathematics · 2017 · Paper 2Calculate the mean and variance of X.
11. 4(c)5 marks· CAPE Integrated Mathematics · 2017 · Paper 2Given that X ~ Bin(8, 0.65), show that P(X > 1) = 0.99643, correct to five decimal places.
12. 4(d)6 marks· CAPE Integrated Mathematics · 2017 · Paper 2A machine produces plastic bottles with capacity having mean 24.3 ml and standard deviation 0.6 ml, normally distributed. Find the probability that a plastic bottle selected at random has a capacity less than 24 ml.
13. 4(e)(i)3 marks· CAPE Integrated Mathematics · 2017 · Paper 2Using the regression equation \hat{y} = 0.186 + 0.64x, where \hat{y} is weight loss in kilograms and x is number of weeks of exercise, determine the weight loss during the 24th week if no changes were made to the…
14. 4(e)(ii)2 marks· CAPE Integrated Mathematics · 2017 · Paper 2The correlation coefficient, r, was found to be 0.981. Comment on the accuracy of the answer obtained in part (e)(i) above.