S1 May 13 model answers :)

On the box plot 24 was marked it was supposed to be 14 :D 

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Sl MAY t3
1. A meteorologist believes that there is a relationship between the height above sea level,
ft m, and the air temperature, t
oC. Data is collected at the same time from 9 diflerent
places on the same mountain. The data is summarised in the table below.
h t400 1 100 260 840 900 550 1230 100 770
t 3 10 20 9 10 l3 5 24 16
[You may assume that Zh:7150, ) r:t to, >h'z :7171s00, >)P 1116'
>th - 64980 and S,, 371.561
(a) Calculate S,,, and S,,,,. Give your answers to 3 significant figures'
(b) Calculate the product moment corelation coefficient ior this data.
(c) State whether of not your value supports the use of a regression equation to predict the
air temperature at different heights on this mountain. Give a reason for your answer.
(d) Find the equation of the regression line ol I on ft giving your answer in the form
7: o+ bh.
(e) Interpret the value of b.
(f) Estimate the difference in air temperature between a height of 500 m and a height of
1000 m.
. (2)
=- -O'q 52*
c) e\es/ r rS chse -16
-SuJ)est co-3tt"'e-
d) b. StX
= -o.ol5oa+

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oc. Yt
- O 'OrS
{x ea",'-. t^.*i:J, t^o.6"^ 1rl*, ttn - *c"^e
4+rrts bJ 6.ot5 .
-1 .S" c a\rf{err.. u- .…read more

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The marks of a group of female students in a statistics test are summarised in Figure I
10 20 30 40 50 60 '70 80 90 100
Figure 1
(a) Write down the mark which is exceeded by 7 5o/o of the female students'
The marks of a group of male students in the same statistics test are summarised by the
stem and leaf diagram below.…read more

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In the space provided on Figure 1 draw a box plot to represent the marks ofthe male
students, indicating clearly any outliers.
(d) Compare and contrast the marks of the male and the female students.
q,) z5
b) A=31 Qr tn + 8h, +(.
= 1--15
Q, |-^ = r5.5 tlbh= 5l
tnacLrcrr1 = 5\, I@.A = ln-
c> l.,^*r t.r.,..t. . +6 - t.Sx\a - 20'5 -,lt rs 6(,1
v?W lrr.ttt = 63+l:Sxlt = 88.…read more

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In a company the 200 employees are classified as full{ime workers, part-time workers or
The table below shows the number of employees in each category and whether they walk
to work or use some form oltransporl.
Walk Transpolt +.rt.r,L
Full{ime worker 2 8 l()
Part-time worker 35 15 lro
Contractor 30 50 go
+-+-& 6+ 133 ILOL)
The events F, H and C are that an employee is a full-time worker, part-time worker or
contractor respectively.…read more

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The following table summarises the tifires, I minutes to the nearest minute, recorded for a
group of students to complete an exam.
ls-s e3 33 +o-s s3
Time (minutes) r ll 20 21 25 26-30 3l - 35 36 45 46-60
Number of students f, 6l 88 16 l3 1l l0
[You *,9.…read more

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E t' ,.t., g::O.S = 3A
t=r s At
62- l{tr2 I so
-'. @z- -- Lz.+ (3te)
- to.s
c-) -F_ o,
r,,,,, j
ol-ro-5= 5Q_
o So Lz lO 62-
:) o, =
ftxrc +lo's
tA'6 Csr)
r 'r1.5
2S'S :ft' ',
Gs = 2S'S
lO-Z = tS.S-t8'6 = 6'9\ (:sp)
e) dc.{z\ rs haaur\3 post
+) or- , olrr arL. \cA effi
nA-c.c^n, rwc-.I. r^ro u}l cul.l
orlso nCJ.fCl- b.,f $, rr.^.…read more

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A biased die with six faces is rolled. The discrete random variable x represents the score
on the uppermost face. The probability distribution of Xis shown in the table be1ow.
.x I 2 3 4 5 6
P(X: x) o a a b h 0.3
(a) Given that E(-l') :4.2 find the value of a and the value of D'
(b) Show that E(X2) -- 20.4
(c) Find Var(5 - 3,1)
A biased die with five faces is rollcd.…read more

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VCx) = 6(xz) -E(r)' = 20,t|-.+.2_z = L.+L
d) 5L= I r. [-=O.L
T) P(s,..,.…read more

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The weight, in grams, of beans in a tin is normally distributed with mean p and standard
deviation 7.8
Given that 10% of tins contain less than 200 g, find
(a) the value ofp
(b) the percentage oftins that contain more than 225 g ofbeans.
The machine settings are adjusted so that the weight, in grams, of beans in a tin is normally
distributed with mean 205 and standard deviation o.…read more


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