‫ م‬0202 / 0202 ‫) المتخان شهادة إمتام الدراسة الجانوية العامة‬6( ‫منوذج اسرتشادى‬

‫ ثالث ساعات‬: ‫الزمن‬ ) ‫( الشعبة األدبية‬ ‫ اإلحصاء باللغة االجنليزية‬: ‫املادة‬

First: Multiple choice questions” one mark for each item”

The scatter diagram representing strong inverse correlation between x , y
(1)
is ………….

(a) (b) (c) (d)

When drawing the scatter diagram between two variables x , y. If all the
(2) points lie on a straight line whose slope is positive , then the correlation
between x , y is ………….
(a) nihilistic (b) inverse weak (c) inverse perfect (d) direct perfect

The following data represents the marks of Stem Leaf

15 students in a monthly test represented by 1 m 3 3 5 8 9
(3) a stem and leaves diagram and the final mark 2 0 1 1 3 5 7
is 30, if the range for this data equals 18, 3 0 0 0
then m = …………. Key 13 = 1|3
(a) 0 (b) 1 (c) 2 (d) 3

(4) If Z is a standard normal random variable, then P (| | 1.75) = ………….

(a) 0.4599 (b) 0.9198 (c) 0.4554 (d) 0.9108

A box contains 9 cards numbered from 1 to 9. If a card is drawn at random

(5) and the number written on the card is observed, if A is a simple event,
then A may be the event of appearing a number ………….
less than or
(a) divisible by 7 (b) (c) less than 7 (d) greater than 7
equal to 7

1
 If A and B are two mutually exclusive events in a sample space of a random
(6) experiment, P(A) = 2 P(B) , the probability of occurring at least one of them
= 0.9 , then P(A – B) = ………….
(a) 0.1 (b) 0.3 (c) 0.6 (d) 0.9

If the following data represents the weights of Stem Leaf

11 competitors in a weightlifting competition 60 0 1 2 2 4
(7) (in kilograms weight unit) represented by stem 70 0 1 1 3
and leaves plot, then the semi-interquartile 80 0 1
range for this data = …………. Key 70.3 = 70|3
(a) 5.05 (b) 10.1 (c) 60.2 (d) 70.3

If Z is a standard normal random variable ,

(8)
then P (Z 1) = ………….
(a) 0.1587 (b) 0.3413 (c) 0.5 (d) 0.8413

A sample size 64, if its standard deviation is 12 using a confidence level of

(9)
95% , then the estimation error equals ………….
(a) 1.2 (b) 1.44 (c) 1.96 (d) 2.94

If X is a normal random variable its mean is µ , its standard deviation is

(10)
σ = 6.4 and P (X  68) = 0.1056 , then µ = ………….
(a) 50 (b) 55 (c) 57 (d) 60
Second: Multiple choice questions” two marks for each item”

If the upper limit of a confidence interval is 31.96 , its mean equals 30 and
(11) its standard deviation equals 7 using a confidence level of 95% ,
then the sample size equals ………….
(a) 25 (b) 36 (c) 49 (d) 64

If the regression line equation is: ̂ = 7 – 0.8 x , then the expected value of y
(12)
when x = 5 is ………….
(a) 2 (b) 3 (c) 5 (d) 7

2
 If X is a continuous random variable whose probability density function is:

(13)
{ , then the value of k = ………….

(a) (b) (c) (d) 1

The following frequency table shows the temperatures during 60 days in

one of the governorates of Egypt :
(14) The temperatures 16– 18– 20– 22– 24– 26– 28– Total
No. of days 4 7 10 18 9 7 5 60
then the lower quartile for these temperatures = ………….
(a) 2.25 (b) 20.8 (c) 23 (d) 25.3

If X is a discrete random variable whose probability distribution is defined

(15) by the function: f (x) = , where x {- 2 , 1 , 2 , m},
then the value of m = ………….
(a) -1 (b) 0 (c) 3 (d) 4

100 students study in an educational languages institute, 60 students study

English, 50 students study French and 35 students study both. A student is
(16)
chosen randomly from this institute, then the probability that the student
studies English knowing that he studies French = ………….
(a) 0.583 (b) 0.417 (c) 0.7 (d) 0.8

In a study of the relation between two variables x , y if:

(17) ∑ ∑ ∑ ∑ ∑ ,n=6,
then Pearson’s correlation coefficient between x , y ………….
(a) - 0.94 (b) - 0.49 (c) 0.49 (d) 0.94

3
 In a study of the relation between two variables x, y, if ∑ ∑ ,
(18) n = 5 and the regression line equation of y on x is ̂ = 1.5 x + k ,
then k = ………….
(a) - 7.5 (b) - 1.5 (c) 1.5 (d) 7.5

A teacher conducted an
Arabic language test to 100 boys
and 100 girls, the maximum mark of
the exam was 45 mark.
If the opposite cumulative frequency
(19)
curves illustrate the performance of
each group, then the appropriate box
plot representation for this distribution
is: ………….

Girls
(a) (b)
Boys

0 10 20 30 40 50 60
0

(d)
(c)

A bag contains 6 blue balls and 4 red balls. If two balls are drawn one after
(20) the other without replacement, then the probability that the first ball is red
and the second ball is blue = ………….
(a) (b) (c) (d)

4
 In a study for the relationship between the levels of the subjects of History
and Geography. If the grades of six students are as follows:
(21) History (x) Excellent Good Very Good Pass Weak Good

Geography (y) Good Weak Pass Excellent Very Good Pass

then the Spearman’s rank correlation coefficient = ………….
(a) - 0.77 (b) - 0.41 (c) 0.41 (d) 0.77

If A and B are two independent events in a sample space of a random

(22)
experiment, such that P(A) = 0.6 , P(B) = 0.2 , then P(A B) = ………….
(a) 0.8 (b) 0.68 (c) 0.32 (d) 0.12

If the following figure shows the box plot of the

(23) marks of an exam for a group of students,
12 14 18 24 27
then the second quartile = ………….
(a) 27 (b) 24 (c) 18 (d) 14

If X is a discrete random variable whose expectation = 0.6 ,

(24)
∑ = 4.36 , then the standard deviation for it equals ………….
(a) 5 (b) 4 (c) 3 (d) 2

The opposite figure is the double Minimum Stem Maximum

representation of stem and leaf for 6 8 9 3 1 9
the maximum and the 1 3 3 2 1 0 2 2 8 2 9 5 9
minimum temperatures in 14 1 2 0 3 2 5 6 4 7 9
(25)
governorates. The absolute
4 1 2
difference between the medians of
the maximum and minimum
Key: 19 means 9 | 1 | 3 means13
temperatures equals ………….
(a) 12 (b) 33.5 (c) 55 (d) 21.5

5
 The critical value corresponding to the 95% confidence level using the
(26)
standard normal distribution = ………….
(a) 1.96 (b) 0.474 (c) 0.475 (d) 0.477

If the regression line equation between x , y is: ̂ = 2.564 x + 35.35

(27) and the table value of y is 356 when x = 120,
then the error in the value of y = ………….
(a) 17 (b) 15 (c) 13.97 (d) 12.97

If the corresponding representation Stem Leaf

is a stem and leaf diagram for 23 4 5
a collection of data , 24 4 7 9
(28) 25 0 4 8 8
then the semi-interquartile range = …………. 26 3 8 9
27 1 2 5
Key 24|7 = 24.7
(a) 1.1 (b) 24.7 (c) 26.9 (d) 25.8

If two regular dice are rolled once, then the probability of appearing the
(29) number 5 on the two upper faces knowing that the same number is
appeared = ………….
(a) (b) (c) (d)

The probability of a team to win in a football match is 0.6 , if the team plays
(30)
7 matches, then the probability of its winning 4 match only ………….
(a) 0.209304 (b) 0.290304 (c) 0.290403 (d) 0.390204

If opposite table represents the

Mathematics Statistics
expectation and the standard deviation Expectation 70 96
(31) for the marks of a group of students in Standard
7 8
deviation
mathematics and statistics ,then the
dispersion in mathematics exam ………. the dispersion in statistics exam.
(a) < (b) (c) > (d)
6
 The opposite table shows the probability
xr 2 3 11
(32) distribution for the random variable X,
f (xr)
then the mean ( ) = ………….
(a) 4 (b) 8 (c) 16 (d) 20

If the monthly income of 1000 families in a village is a normal random

(33) variable with mean 180 pounds , and standard deviation 20 pounds, then the
number of families whose income exceeds 150 pounds …………. family.
(a) 433 (b) 117 (c) 833 (d) 933

Third: essay questions “two marks for each question”.

Two soldiers A and B shoot a single shot at a target. If the probability that
the first soldier hits the target is 0.4 , the probability that the second soldier
(34) will hit the target is 0.7 and the probability of hitting the target is 0.82
Find the probability that only one of them will hit the target.

If X is a normal random variable with mean = 48 and standard deviation

(35) = 5 . Find the value of k, such that P (X > k) = 0.1844