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A company director decides to survey staff about changes to the company calendar. The company has staff in 4 different job roles 72 managers, 108 drivers, 180 administrators and 360 warehouse staff. The director decides to take a stratified sample. (a) Write down one advantage of using a stratified sample rather than a simple random sample for this survey. (1) (b) Find the number of staff in each job role that will be included in a stratified sample of 40 staff. (3) (c) Describe how to choose managers for the stratified sample. (2) (Total for question = 6 marks)
Sara is investigating the variation in daily maximum gust, t kn, for Camborne in June and July 1987. She used the large data set to select a sample of size 20 from the June and July data for 1987. Sara selected the first value using a random number from 1 to 4 and then selected every third value after that. (a) State the sampling technique Sara used. (1) (b) From your knowledge of the large data set, explain why this process may not generate a sample of size 20. (1) The data Sara collected are summarised as follows (c) Calculate the standard deviation. (2) (Total for question = 4 marks)
Estimate the percentage of these motorists who were delayed by the roadworks for between 8.5 and 13. minutes. (5) (Total for question = 5 marks)
The following table summarises the times, t minutes to the nearest minute, recorded for a group of students to complete an exam. [You may use f t^2 = 134281.25] (a) Estimate the mean and standard deviation of these data. (5) (b) Use linear interpolation to estimate the value of the median. (2) (c) Show that the estimated value of the lower quartile is 18.6 to 3 significant figures. (1) (d) Estimate the interquartile range of this distribution. (2) (e) Give a reason why the mean and standard deviation are not the most appropriate summary statistics to use with these data.
Events A , B and C are such that ยท P( A or C ) = 0. ยท the probability that none of the events occur is 0. ยท the probability that exactly two of the events occur is 0. ยท A and B are independent ยท P( B ) = P( A ) + 0. The Venn diagram represents the events A , B and C and their associated probabilities p , q , r , s , t and u
(a) Write down the value of u (1) (b) Find the value of r (2) (c) Find (i) the value of p (ii) the value of q (iii) the value of s (iv) the value of t (4) (Total for question = 7 marks)
where q is a probability. (a) Find the value of q (1) Karen spins the spinner repeatedly until she either gets a 7 or she has taken 4 spins. (b) Show that the probability that Karen stops after taking her 3rd^ spin is 0. (2) The random variable S represents the number of spins Karen takes. (c) Find the probability distribution for S (4) The random variable N represents the number of times Karen gets a 7 (d) Find P( S > N ) (1) (Total for question = 8 marks)
The random variable X ~ B(20, 0.37)
The random variable X ~ B (27, 0.35) (a) Find (i) P ( X = 10) (ii) P (12 โค X < 15) (3) Historical records show that the proportion of defective items produced by a machine is 0. Following a maintenance service of the machine, a random sample of 60 items is taken and 3 defective items are found. (b) Carry out a suitable test to determine whether the proportion of defective items produced by the machine has decreased following the maintenance service. You should state your hypotheses clearly and use a 5% level of significance. (4) (c) Write down the p -value for your test in part (b) (1) (Total for question = 8 marks)
