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    This is my answers to the S1 Exam this morning, please correct me if some are incorrect. I hope this helps!

    1.

    a) r = 0.498 (2 Marks)

    b) There is a moderate positive correlation between ... and ... (2 Marks)

    2. a) mean = 68.3 variance = 2.46 and 2.42 was also allowed (4 Marks)

    b) mean = 2.69 variance = 3.81 x 10^-3 (2 Marks)

    3.

    a) Complete the table (2 Marks)

    b) i) 0.56 ii) 0.20 (3 Marks)

    c) i) 0.25 ii) 0.90 (5 Marks)

    d) 0.084 (4 Marks)

    4.

    a) Plot the remaining four points (2 Marks)

    b) i) y = 0.405x + 1.3 (6 Marks)

    ii) Explain this in context of the question (3 Marks)

    c) when x = 15, y = 7.4 (1 Mark)

    d) i) Residual = -0.6 (2 Marks)

    ii) The residuals only show the connection between the values of y predicted by the line of regression and the actual values of y. Itdoes not look at the relationship between x and y or the sum of the residuals will equal 0 (1 Mark)

    5.

    a) i) 0.871 ii) 0.309 iii) 0.191 (6 Marks)

    b) i) 1.175 (2 Marks)

    ii) mean = 9.06 and standard deviation = 0.162 (4 Marks)

    6. a) i) 0.695 ii) 0.879 iii) 0.562 iv) 0.131 (9 Marks)

    b) 0.0478, It is assumed that the sample is random (4 Marks)

    7. a) 0.0418 (4 Marks)

    b) i) 304.6 +- 2.2 = [302.4, 306.8] (4 Marks)

    ii) First claim is likely correct, as 300 is below the lower limit of the confidence interval

    Second claim is very likely to be incorrect as the mean minus one standard deviation is below 300 (4 Marks)
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    r was 0.9 something, coeff of x in q4 was 3, a was 18 something, last binomial question p(45>X>35) was 0.8 something, the answer to the question about two who ever 41-61 & Band 1 or 2, and two who were 62 + and in band 0 or something was P(41-61&P(B1orB2))^2 * P(61+&B0) * 6
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    yeah r was not 0.498
 
 
 
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