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6683
Edexcel GCE
Statistics S1
Advanced/Advanced Subsidiary
Wednesday 15 January 2003 ( Morning
Time: 1 hour 30 minutes
Materials required for examination Items included with question papers Answer Book (AB16) Nil Graph Paper (ASG2)
Mathematical Formulae (Lilac)
Candidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Thus candidates may NOT use calculators such as the Texas Instruments TI 89, TI 92, Casio CFX 9970G, Hewlett Packard HP 48G.
Instructions to Candidates
In the boxes on the answer book, write the name of the examining body (Edexcel), your centre number, candidate number, the unit title (Statistics S1), the paper reference (6683), your surname, other name and signature.
Values from the statistical tables should be quoted in full. When a calculator is used, the answer should be given to an appropriate degree of accuracy.
Information for Candidates
A booklet Mathematical Formulae and Statistical Tables is provided.
Full marks may be obtained for answers to ALL questions.
This paper has seven questions. Pages 6, 7 and 8 are blank.
Advice to Candidates
You must ensure that your answers to parts of questions are clearly labelled.
You must show sufficient working to make your methods clear to the Examiner. Answers
without working may gain no credit.
1. The total amount of time a secretary spent on the telephone in a working day was recorded to the nearest minute. The data collected over 40 days are summarised in the table below.
Time (mins)90139140149150159160169170179180229No. of days81010444
Draw a histogram to illustrate these data
(4)
2. A car dealer offers purchasers a three year warranty on a new car. He sells two models, the Zippy and the Nifty. For the first 50 cars sold of each model the number of claims under the warranty is shown in the table below.
ClaimNo claimZippy3515Nifty4010
One of the purchasers is chosen at random. Let A be the event that no claim is made by the purchaser under the warranty and B the event that the car purchased is a Nifty.
(a) Find P(A ( B).
(2)
(b) Find P( EMBED Equation.3 ).
(2)
Given that the purchaser chosen does not make a claim under the warranty,
(c) find the probability that the car purchased is a Zippy.
(2)
(d) Show that making a claim is not independent of the make of the car purchased.
Comment on this result.
(3)
A drinks machine dispenses coffee into cups. A sign on the machine indicates that each cup contains 50 ml of coffee. The machine actually dispenses a mean amount of 55 ml per cup and 10% of the cups contain less than the amount stated on the sign. Assuming that the amount of coffee dispensed into each cup is normally distributed find
(a) the standard deviation of the amount of coffee dispensed per cup in ml,
(4)
(b) the percentage of cups that contain more than 61 ml.
(3)
Following complaints, the owners of the machine make adjustments. Only 2.5% of cups now contain less than 50 ml. The standard deviation of the amount dispensed is reduced to 3 ml.
Assuming that the amount of coffee dispensed is still normally distributed,
(c) find the new mean amount of coffee per cup.
(4)
15,14,16,15,17,16,15,14,15,16,17,16,15,14,16,17,15,25,18,164. A restaurant owner is concerned about the amount of time customers have to wait before being served. He collects data on the waiting times, to the nearest minute, of 20 customers. These data are listed below.
(a) Find the median and inter-quartile range of the waiting times.
(5)
An outlier is an observation that falls either 1.5 ( (inter-quartile range) above the upper quartile or 1.5 ( (inter-quartile range) below the lower quartile.
(b) Draw a boxplot to represent these data, clearly indicating any outliers.
(7)
(c) Find the mean of these data.
(2)
(d) Comment on the skewness of these data. Justify your answer.
(2)
5. The discrete random variable X has probability function
where k is a positive constant.
(a) Show that k = 0.25.
(2)
(b) Find E(X) and show that E(X 2) = 2.5.
(4)
(c) Find Var(3X 2).
(3)
Two independent observations X1 and X2 are made of X.
(d) Show that P(X1 + X2 = 5) = 0.
(1)
(e) Find the complete probability function for X1 + X2.
(3)
(f) Find P(1.3 ( X1 + X2 ( 3.2).
(3)
6. The chief executive of Rex cars wants to investigate the relationship between the number of new car sales and the amount of money spent on advertising. She collects data from company records on the number of new car sales, c, and the cost of advertising each year, p (000). The data are shown in the table below.
YearNumber of new car sale, cCost of advertising (000), p19904240120199143801261992442013219934440134199444301371995452014419964590148199746601501998470015319994790158
(a) Using the coding x = (p 100) and y = EMBED Equation.3 (c 4000), draw a scatter diagram to represent these data. Explain why x is the explanatory variable.
(5)
(b) Find the equation of the least squares regression line of y on x.
[Use (x = 402, (y = 517, (x2 = 17 538 and (xy = 22 611.]
(7)
(c) Deduce the equation of the least squares regression line of c on p in the form c=a+bp.
(3)
(d) Interpret the value of a.
(2)
(e) Predict the number of extra new cars sales for an increase of 2000 in advertising budget. Comment on the validity of your answer.
(2)
N6894 PAGE 4
N10623A This publication may only be reproduced in accordance with Edexcel copyright policy.
Edexcel Foundation is a registered charity. 2003 Edexcel
N10632A PAGE 2
N10623A PAGE 5
END
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