A King Abdulaziz University STAT 110 1433/1434 Faculty of Sciences Second Exam First Term Statistics Department Exam Time: 90 minutes Date: 17/01/1434H Please mark all your answers on the answer sheet provided to you. Only the answer sheet will be graded. Choose the best answer for each of the following questions. Good Luck The frequency distribution shown below represented the grades of 60 students in Statistics last semester. If a student was selected randomly. Answer questions (1 -­‐ 3). Grade A B C D F Total Frequency 8 14 27 7 4 60 1-­‐ Find the probability that the selected student got a grade D in Statistics. a) 0.550 b) 0.117 c) 0.883 d) 0.450 2-­‐ Find the probability that the selected student did not get a grade A in Statistics. a) 0.867 b) 0.133 c) 1 d) 0 3-­‐ Find the probability that the selected student did not get grade B nor grade F in Statistics. A) 0.300 b) 0.016 c) 0.700 d) 0.984 4- Which of the following distribution is a probability distribution?
a)
b)
!
!(!)
1
0.2
2
0.4
3
0.6
4
0.8
!
!(!)
5
1.0
c)
-2
0.2
-1
0.2
0
0.2
1
0.2
2
0.2
1
1
2
2
3
3
4
4
d)
!
!(!)
-1
-0.2
0
-0.4
1
1.0
2
0.2
!
!(!)
3
0.4
0
0
5-­‐ How many outcomes would be in the figure below? Red Red White Red White White a) 1 ©2013 STAT 110 Team b) 2 A c) 4 Red White Red White Red White Red White d) 8 Page 1 If a random variable ! has the discrete probability distribution as shown below, then answer questions (6 - 9)
!
1
2
3
4
5
6
!(!)
k
0.32
0.09
0.17
0.04
0.03
6- Find the missing probability, !.
a) 0.65
b) 1.35
c) 0.35
d) 1.65
7- Find the mean of the distribution, !.
a) 2.32
b) 1.86
c) 1.36
d) 7.24
8- Find the variance of the distribution, !! .
a) 1.36
b) 2.32
c) 7.24
d) 1.86
9- Find the standard deviation of the distribution, !
a) 7.24
b) 1.36
c) 1.86
d) 2.32
Use the available information to answer questions (10–15): ! = !, ! = !"!, ! = !", !" = !"#", !! = !"#$%, !! = !"" 10-­‐ Find the Pearson correlation coefficient, !! . a) −0.51 b) −0.49 c) 0.49 d) 0.51 11-­‐ The value of the correlation coefficient obtained in previous question can be interpreted as follows: There is a ………… linear relationship between the variables ! and !. a) moderate positive b) weak positive c) moderate negative d) weak negative 12-­‐ Find the slope of the regression line, !. a) 0.05 b) 3.65 c) −0.05 d) −3.65 13-­‐ Find the !_intercept, !. a) −0.05 b) 0.05 c) −3.65 d) 3.65 14-­‐ Find the equation of the regression line. a) ! ! = 0.05 + 3.65! b) ! ! = −3.65 − 0.05! c) ! ! = −0.05 + 3.65! d) ! ! = 3.65 + 0.05! 15-­‐ Predict the value of ! when ! = !" a) −6.6 b) 6.6 c) 215.4 d) 215.3 16-­‐ The line of ………… means the line that the sum of the squares of the vertical distances from each point to this line is at a minimum. a) regression b) best fit c) correlation d) scatter ©2013 STAT 110 Team A Page 2 17-­‐ The probability that the value of correlation coefficient lies between and includes +1 and -­‐1 is always ………… a) 1 b) zero c) unknown d) certain event If a coin was tossed two times. Answer questions (18 – 24) 18-­‐ How many trials are there? a) 1 b) 2 c) 3 d) 4 19-­‐ How many outcomes in each trial are there? a) 1 b) 2 c) 3 d) 4 20-­‐ The number of all possible outcomes of tossing two coins is … a) 1 b) 2 c) 3 d) 4 21-­‐ Find the sample space. a) ! = {!"} b) ! = {!!, !!} c) ! = {!!, !", !". !!} d) ! = {!!, !", !!} 22-­‐ the simple event is ………… a) ! = {!!} b) ! = {!!, !", !"} c) ! = {!", !", !!} d) ! = {!", !"} 23-­‐ the compound event is ………… a) ! = {!!} b) ! = {!"} c) ! = {!!} d) ! = {!", !"} 24-­‐ Find the probability of getting exactly two heads. a) 0.500 b) 0.750 c) 0.250 d) 1 A person was selected at random from a group of people classified according to their job and whether they are married or not. The findings are summarized in the table below. Answer questions (25 – 27). Job Doctor Teacher Engineer Total Marriage Yes 48 74 56 178 No 66 28 83 177 Total 114 102 139 355 25-­‐ Find the probability that the selected person is married. a) 0.321 b) 0.499 c) 0.501 d) 0.392 26-­‐ Find the probability that the selected person is not married or a Doctor. a) 0.634 b) 0.820 c) 0.186 d) 0.160 27-­‐ Find the probability that the selected person is a Teacher or an Engineer. a) 0.887 b) 0.113 c) 0.321 d) 0.679 ©2013 STAT 110 Team A Page 3 28-­‐ A box contains 7 green pens, 5 blue pens, 9 black pens, and 3 red pens. One pen was selected and its color noted, then it is replaced. Second pen was selected and its color noted. Find the probability that the selected pens are black and then green. a) 0.667 b) 0.109 c) 0.333 d) 0.891 Five students were examined in two subjects (Statistics and Mathematics) is there a relationship between their Statistics grades and Mathematics grades. Based on the results given in the table below, answer questions (29 -­‐ 30). Statistics grades (X) A D B C F Mathematics grades (Y) D C A F B 29-­‐ Find the value of the correlation coefficient between the Statistics grades and the Mathematics grades. a) −0.20 b) −1.20 c) 1.20 d) 0.20 30-­‐ The value of the correlation coefficient in previous question reveals that there is ………… relationship between the Statistics grades and the Mathematics grades. a) strong negative b) weak positive c) strong positive d) weak negative ©2013 STAT 110 Team A Page 4 Formulas: !
Pearson linear correlation coefficient: r! =
!
!!
Spearman rank correlation coefficient: r! = 1 −
!
!" !( !)( !)
!
! ! [!
!!
!(!! !!)
!! !( !)! ]
Equation of regression line: y ! = a + bx y intercept of the regression line: a =
! !(!)( !)
!
Slope of the regression line: b =
Classical probability: P E =
!
!(!)
!(!)
!" !( !)( !)
!
!! !
! !
!
Empirical probability: P E = !
Rule for complementary events: P E + P E = 1 Probability of mutually exclusive: P A or B = P A + P(B) Probability of not mutually exclusive: P A or B = P A + P B − P A and B Probability of independent: P A and B = P A ∗ P(B) Mean of a probability distribution: µμ =
X P(X) Variance of a probability distribution: σ! =
X ! P(X) − µμ! Standard deviation of a probability distribution: σ = σ! ©2013 STAT 110 Team A Page 5 ©2013 STAT 110 Team A Page 6 1-­‐ B 2-­‐ A 3-­‐ C 4-­‐ B 5-­‐ D 6-­‐ C 7-­‐ A 8-­‐ D 9-­‐ B 10-­‐ C 11-­‐ B 12-­‐ A 13-­‐ D 14-­‐ D 15-­‐ B 16-­‐ B 17-­‐ A 18-­‐ B 19-­‐ B 20-­‐ D 21-­‐ C 22-­‐ A 23-­‐ D 24-­‐ C 25-­‐ C 26-­‐ A 27-­‐ D 28-­‐ B
29-­‐ A 30-­‐ D ©2013 STAT 110 Team Answer Key Form A A Page 7