OCR AS Level Further Mathematics B (MEI) Y416-01 Statistics b June 2022 QUESTION PAPER

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Each working day, Beth takes a bus to her place of work. She believes that the mean time that her journey takes is 30 minutes. In order to check this, Beth selects a random sample of 8 journeys. The... times in minutes for these 8 journeys are as follows. 31.9 28.5 35.9 31.0 30.2 34.9 28.9 31.3 (a) What assumption does Beth need to make in order to construct a confidence interval for the mean journey time based on the t distribution? [1] (b) In this question you must show detailed reasoning. Given that the assumption in part (a) is valid, determine a 95% confidence interval for the mean journey time. [7] (c) Explain whether the confidence interval suggests that Beth may be correct in the belief that her mean journey time is 30 minutes. [2] 2 The continuous random variable X has cumulative distribution function given by ( ) , , , x b a x a x a a x b x b 0 1 1 2 = G G - - F * where a and b are constants with 0 1 1a b. (a) Find P X a( ) b 2 1 a 1 + k. [2] (b) Sketch the graph of the probability density function of X. [3] (c) Find the variance of X when a = 2 and b = 8. [Show More]

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