Tutorial Answers T2 3

8/2/2019 Tutorial Answers T2 3

1/4

Tutorial Answers

Tutorial 2

1. c. 30% of the elements in this sample belong to B

d. 70% of the elements in this sample belong to A or C.

2. ii) k=6 (No. of classes)

iii)

02468

10121416

24.5 34.5 44.5 54.5 64.5 74.5 84.5 94.5 105

Scores

Frequecny

iv) a. 4 students will fail

b. X 85

3. b. Mean = 1.9 Mode =1 Median = 1.5

c.Range =5,213

13=== QQIQR

s= 1.4474

d. sk= 0.829The data is slightly skewed to the right. That means more taxis are with

less passengers.

4. a. Mean = 2127.33 Median =123

b. Median is more appropriate here since there is an outlier, i.e. USA :15613

and mean is more influenced by the outlier

c. Range = 15554d. IQR= 1385

5.

Temperature m f fx fx2

96.5 96.8 96.65 1 96.65 9341.2225

96.9 97.2 97.05 8 776.4 75349.6297.3 97.6 97.45 14 1364.3 132951.03597.7 98.0 97.85 22 2152.7 210641.695

98.1 98.4 98.25 19 1866.75 183408.1875

98.5 98.8 98.65 32 3156.8 311418.32

98.9 99.2 99.05 6 594.3 58865.41599.3 99.6 99.45 4 397.8 39561.21

106 10405.7 1021536.705


2/4

a. Mean = 98.17

b. S= 0.621s

c. Q197.8 Q398.6

6. a. New mean = 76.4

New Range = 12Median = 78

b. New mean = 75.2

We cannot determine the new range and new median since the largest and

smallest values cannot be determined based the given information.

7. a Mean =52

R = 14

s= 5.89

b. 50=

XY 22

XY ss = XY RR=

c. xy2

1= ,

22

4

1

xyss = XY RR

2

1=

8. a. k=2

From Chebyshevs Theorem, there are at least 75% of its flight

between the two cities arrive anywhere between 2.6 minutes late and 8.2

minutes late.

b. k=5

From Chebyshevs Theorem, there are at least 96% of its flight betweenthe two cities arrive anywhere between 1.6 minutes early and 12.4 minutes

late.

9. a. k=1

By using Empirical rule, there are approximately 68% of heights of the

women are between 61.1in and 66.1in.

b. k=3 By using Empirical rule, there are approximately 99.7% of heights of

the women are between 61.1in and 66.1in.

10. For Everlast, 50 = , 2 = .For Endurance, 50 = , 6 = .


3/4

Since both brands have same mean life and it is larger than the labeled life, so the

brand with smaller standard deviation is the better choice, i.e. Everlast. This is

because the smaller standard deviation means the data are closer to the mean.

11. VA= 5.22% VB= 6.73% Since Va< Vb the first student is relatively more

consistent in doing these tests

12. Calories: mean = 380 median = 350 1st quartile = 260 3rd quartile = 510Fat: mean = 15.8 median = 19 1st quartile = 8 3rd quartile = 22

(b) Calories: variance = 12800 standard deviation = 113.1 range = 290

interquartile range = 250 CV = 29.77%

None of the Z scores are less than -3 or greater than 3. There is no outlier in calories.

Fat: variance = 52.82 standard deviation = 7.3 range = 18.5

Interquartile range = 14 CV = 46.04%

None of the Z scores are less than -3 or greater than 3. There is no outlier in fat.

(c) Calories are slightly right-skewed while fat is slightly left-skewed.

(d) The mean calories is 380 while the middle ranked calorie is 350. The average scatter

of calories around the mean is 113.14. 50% of the calories are scattered over 250while the difference between the highest and the lowest calories is 290.

The mean fat is 15.79 grams while the middle ranked fat is 19 grams. The average

scatter of fat around the mean is 7.27 grams. 50% of the fat is scattered over 14

grams while the difference between the highest and the lowest fat is 18.5 grams.

Tutorial 3

4. P(A) = 12 / 45

P(AA) = (12 / 45) (11 / 44)

5. a. b. 1/16 c. 3/8

6. 240

7. a. 1/ 169 b. 1/221

8. a. A and B are not mutually exclusive sinceA B ={2} .

b. A and B are not independent

c. P(A) = 5/8 = .625 P(B) = 5/8 = .625

9. a. i. 0.2958

ii. 0.6137


4/4

iii. 0.6899

iv. 0.4377

v. 0.6215

10. 0.40951

11. a. 0.18 b. 0.77 c. 0.31 d. 0.23 e. 0574 f. 0.561

12. i. 0.35 ii. 0.75 iii. 0.4286

13. a. 0.6456 b. 0.7007

Documents

Tutorial Answers T2 3