# Advanced/Advanced Subsidiary. You must have: Mathematical Formulae and Statistical Tables (Blue)

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2 1. A price comparison website publishes data on the cost per month, c, and the level of satisfaction, s, of a random sample of six internet service providers. A low value of s corresponds to a low level of satisfaction. The data are given in the table below. Internet service A B C D E F provider c s (You may use c 111, c , s 21, s 2 9, cs = 380, S cc = 321.5) (a) Calculate the value of S cs and the value of S ss (3) (b) Calculate the product moment correlation coefficient for these data. (2) Brad is not satisfied with his current internet service and decides to change his provider. He decides to pay a lot more for his new internet service. (c) On the basis of your calculation in part (b), comment on Brad s decision. Give a reason for your answer. (2) 2 *P43140A0228*

3 Question 1 continued Q1 (Total 7 marks) *P43140A0328* 3 Turn over

4 2. A rugby club coach uses club records to take a random sample of 15 players from 1990 and an independent random sample of 15 players from The body weight of each player was recorded to the nearest kg and the results from 2010 are summarised in the table below. Body weight (kg) Number of Players (2010) (a) Find the estimated values in kg of the summary statistics a, b and c in the table below. Estimate in 1990 Estimate in 2010 Mean 83.0 a Median 82.0 b Variance 44.0 c Give your answers to 3 significant figures. (6) The rugby coach claims that players body weight increased between 1990 and (b) Using the table in part (a), comment on the rugby coach s claim. (2) 4 *P43140A0428*

5 Question 2 continued Q2 (Total 8 marks) *P43140A0528* 5 Turn over

6 3. Jean works for an insurance company. She randomly selects 8 people and records the price of their car insurance, p, and the time, t years, since they passed their driving test. The data is shown in the table below. t p (You may use t = 19.5, p = 470, S tp = 6080, S tt = 254, S pp = ) (a) On the graph below draw a scatter diagram for these data. (b) Comment on the relationship between p and t. (c) Find the equation of the regression line of p on t. (2) (1) (4) (d) Use your regression equation to estimate the price of car insurance for someone who passed their driving test 20 years ago. (2) Jack passed his test 39 years ago and decides to use Jean s data to predict the price of his car insurance. (e) Comment on Jack s decision. Give a reason for your answer. (2) p O t 6 *P43140A0628*

7 Question 3 continued *P43140A0728* 7 Turn over

8 Question 3 continued 8 *P43140A0828*

9 Question 3 continued Q3 (Total 11 marks) *P43140A0928* 9 Turn over

10 4. A discrete random variable X has the probability distribution given in the table below, where a and b are constants. x P(X = x) a b Given E(X) = 9 5 (a) (i) find two simultaneous equations for a and b, (ii) show that a = 1 20 and find the value of b. (4) (b) Specify the cumulative distribution function F(x) for x = 1, 0, 1, 2 and 3 (c) Find P(X < 2.5). (2) (1) (d) Find Var(3 2X). (4) 10 *P43140A01028*

11 Question 4 continued *P43140A01128* 11 Turn over

12 Question 4 continued 12 *P43140A01228*

13 Question 4 continued Q4 (Total 11 marks) *P43140A01328* 13 Turn over

14 5. A group of 100 students are asked if they like folk music, rock music or soul music. All students who like folk music also like rock music No students like both rock music and soul music 75 students do not like soul music 12 students who like rock music do not like folk music 30 students like folk music (a) Draw a Venn diagram to illustrate this information. (b) State two of these types of music that are mutually exclusive. (4) (1) Find the probability that a randomly chosen student (c) does not like folk music, rock music or soul music, (d) likes rock music, (e) likes folk music or soul music. (1) (1) (1) Given that a randomly chosen student likes rock music, (f) find the probability that he or she also likes folk music. (2) 14 *P43140A01428*

15 Question 5 continued *P43140A01528* 15 Turn over

16 Question 5 continued 16 *P43140A01628*

17 Question 5 continued Q5 (Total 10 marks) *P43140A01728* 17 Turn over

18 6. A manufacturer has a machine that fills bags with flour such that the weight of flour in a bag is normally distributed. A label states that each bag should contain 1 kg of flour. (a) The machine is set so that the weight of flour in a bag has mean 1.04 kg and standard deviation 0.17 kg. Find the proportion of bags that weigh less than the stated weight of 1 kg. (3) The manufacturer wants to reduce the number of bags which contain less than the stated weight of 1 kg. At first she decides to adjust the mean but not the standard deviation so that only 5% of the bags filled are below the stated weight of 1 kg. (b) Find the adjusted mean. (3) The manufacturer finds that a lot of the bags are overflowing with flour when the mean is adjusted, so decides to adjust the standard deviation instead to make the machine more accurate. The machine is set back to a mean of 1.04 kg. The manufacturer wants 1% of bags to be under 1 kg. (c) Find the adjusted standard deviation. Give your answer to 3 significant figures. (3) 18 *P43140A01828*

19 Question 6 continued *P43140A01928* 19 Turn over

20 Question 6 continued 20 *P43140A02028*

21 Question 6 continued Q6 (Total 9 marks) *P43140A02128* 21 Turn over

22 7. In a large college, 3 3 of the students are male, of the male students are left handed. 5 A student is chosen at random. of the students are left handed and (a) Given that the student is left handed, find the probability that the student is male. (2) (b) Given that the student is female, find the probability that she is left handed. (c) Find the probability that the randomly chosen student is male and right handed. (3) (2) Two students are chosen at random. (d) Find the probability that one student is left handed and one is right handed. (2) 22 *P43140A02228*

23 Question 7 continued *P43140A02328* 23 Turn over

24 Question 7 continued 24 *P43140A02428*

25 Question 7 continued Q7 (Total 9 marks) *P43140A02528* 25 Turn over

26 8. A manager records the number of hours of overtime claimed by 40 staff in a month. The histogram in Figure 1 represents the results. Frequency density Hours of overtime Figure 1 (a) Calculate the number of staff who have claimed less than 10 hours of overtime in the month. (4) (b) Estimate the median number of hours of overtime claimed by these 40 staff in the month. (2) (c) Estimate the mean number of hours of overtime claimed by these 40 staff in the month. (2) The manager wants to compare these data with overtime data he collected earlier to find out if the overtime claimed by staff has decreased. (d) State, giving a reason, whether the manager should use the median or the mean to compare the overtime claimed by staff. (2) 26 *P43140A02628*

27 Question 8 continued *P43140A02728* 27 Turn over

28 Question 8 continued Q8 (Total 10 marks) END TOTAL FOR PAPER: 75 MARKS 28 *P43140A02828*

### Paper Reference(s) 6683 Edexcel GCE Statistics S1 Advanced/Advanced Subsidiary Friday 11 June 2004 Morning Time: 1 hour 30 minutes

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