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Date May 2017 Marks available 1 Reference code 17M.2.sl.TZ1.5
Level SL only Paper 2 Time zone TZ1
Command term Find Question number 5 Adapted from N/A

Question

The table below shows the distribution of test grades for 50 IB students at Greendale School.

M17/5/MATSD/SP2/ENG/TZ1/05

A student is chosen at random from these 50 students.

A second student is chosen at random from these 50 students.

The number of minutes that the 50 students spent preparing for the test was normally distributed with a mean of 105 minutes and a standard deviation of 20 minutes.

Calculate the mean test grade of the students;

[2]
a.i.

Calculate the standard deviation.

[1]
a.ii.

Find the median test grade of the students.

[1]
b.

Find the interquartile range.

[2]
c.

Find the probability that this student scored a grade 5 or higher.

[2]
d.

Given that the first student chosen at random scored a grade 5 or higher, find the probability that both students scored a grade 6.

[3]
e.

Calculate the probability that a student chosen at random spent at least 90 minutes preparing for the test.

[2]
f.i.

Calculate the expected number of students that spent at least 90 minutes preparing for the test.

[2]
f.ii.

Markscheme

1(1)+3(2)+7(3)+13(4)+11(5)+10(6)+5(7)50=23050     (M1)

 

Note:     Award (M1) for correct substitution into mean formula.

 

=4.6     (A1)     (G2)

[2 marks]

a.i.

1.46 (1.45602)     (G1)

[1 mark]

a.ii.

5     (A1)

[1 mark]

b.

64     (M1)

 

Note:     Award (M1) for 6 and 4 seen.

 

=2     (A1)     (G2)

[2 marks]

c.

11+10+550     (M1)

 

Note:     Award (M1) for 11+10+5 seen.

 

=2650 (1325, 0.52, 52%)     (A1)     (G2)

[2 marks]

d.

10their 26×949     (M1)(M1)

 

Note:     Award (M1) for 10their 26 seen, (M1) for multiplying their first probability by 949.

 

OR

1050×9492650

 

Note:     Award (M1) for 1050×949 seen, (M1) for dividing their first probability by their 2650.

 

=45637 (0.0706, 0.0706436, 7.06436%)     (A1)(ft)     (G3)

 

Note:     Follow through from part (d).

 

[3 marks]

e.

P(X90)     (M1)

OR

M17/5/MATSD/SP2/ENG/TZ1/05.f.i/M     (M1)

 

Note:     Award (M1) for a diagram showing the correct shaded region (>0.5).

 

0.773 (0.773372) 0.773 (0.773372, 77.3372%)     (A1)     (G2)

[2 marks]

f.i.

0.773372×50     (M1)

=38.7 (38.6686)     (A1)(ft)     (G2)

 

Note:     Follow through from part (f)(i).

 

[2 marks]

f.ii.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.
[N/A]
c.
[N/A]
d.
[N/A]
e.
[N/A]
f.i.
[N/A]
f.ii.

Syllabus sections

Topic 4 - Statistical applications » 4.1
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