Math

Posted: August 26th, 2021

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Math

Worksheet for Chapter 12

Part A

Question 1. Construct a frequency distribution table

CLASS	FREQUENCY
1 – 8	0
9-12	10
13-15	6
16-19	9
20-23	5

Question 2

1. Construct histogram

•  Construct Stem and leaf plot

STEM	LEAF
0	9
1	0,4,5,0,9,5,6,7,3,3,2,0,4,6,7,8,9,0,7,9,1,2
2	0,1,0,1,1

Question 3

a) Calculate the mean

Mean=μ = (ΣX_i) / N

=447/30

=14.9

b) Calculate the median

9 ,9 ,9 ,10 ,10 ,10 ,10 ,11 ,12 ,12 ,13 ,13 ,14 ,14 ,15 ,15 ,16 ,16 ,17 ,17 ,17 ,18 ,19 ,19 ,19 ,20 ,20 ,21 ,21 ,21

Median=14+15/2   

           =14.5

c) Calculate the mode

The mode is the number with the most number of appearances. In this data, 10 appears 10 times. Thus, the mode is 10

d) Calculate the Standard Deviation

σ = sqrt [Σ(Xi – μ) 2 / N]

μ	Xi – μ	(Xi – μ )2
14.9	10-14.9	24.01
14.9	14-14.9	34.81
14.9	15-14.9	0.01
14.9	10-14.9	24.01
14.9	9-14.9	34.81
14.9	20.14.9	26.01
14.9	21-14.9	37.21
14.9	19-14.9	16.81
14.9	15-19.5	0.01
14.9	16-14.9	1.21
14.9	17.14.9	4.41
14.9	13-14.9	3.61
14.9	13-14.9	3.61
14.9	12-14.9	8.41
14.9	10-14.9	24.01
14.9	9-14.9	34.81
14.9	20-14.9	26.01
14.9	14-14.9	0.81
14.9	16-14.9	2.21
14.9	17-14.9	4.41
14.9	18-.14.9	9.61
14.9	19-14.9	16.81
14.9	21-14.9	37.21
14.9	10-14.9	24.01
14.9	9-14.9	34.81
14.9	17-14.9	4.41
14.9	19-14.9	16.81
14.9	21-14.9	37.21
14.9	11-14.9	15.21
14.9	12-14.9	8.41
		SUM=514.7

SD=SQ MEAN

SD =22.69

Question 4. Is this data from a normal distribution? Why?

This sample is not from a normal distribution. For data to be considered as a normal distribution, the mean, mode, and median must be equal. In the above case, the mean is 14.9, the mode is 10, and the median is 14.5, indicating that the data is not from a sample of normal distribution. Also, for data to be considered as a normal distribution, the histogram must mimic the S-shaped curve.

Question 5. Determine the Z score A Percentile of a Student Who Studied 22 Hours in a Week

Where X=22

Mean=14.9

S D= 22.69

Then Z = 22-14.9/22.69

Z score = 0.313

Percentile

From the normal distribution table, the Z value lies in the 75^th percentile. Thus, this implies that 75% of the observation are distributed around the mean

PART B: CRITICAL THINKING

Question 6. Given the mean of 10 and a median of 14, illustrate if the statement follows or does not follow

Data is normally distributed-Does not follow

Mode of data is 10-Does not follow

Data is skewed to the left-Follow

The standard deviation of the data is 4- Does not follow.

Worksheet for Chapter 6

Part A: Equations and Proportions

Question 1.a)

2/y+5=-3/y-6

2(y-6)=-3(y+5)

2y-12=-3y-15

2y+3y=-15+12

Y=-0.6

Question 1.b)

Solve for S=a1/1-r

(1-r)S=a1

(1-r) = a1/S

1-r=a1/S

R=a1/S+1

Question 1 C)

7*(3X-2)+5 =6*(2X-1)+24

21X – 14+5=12X – 6+24

21X-12X=-6+24+14-5

9X=27

X=3

PART B: Word Problems

Question 1

Weight on earth=360 pounds

Weight on moon =60 pounds

If 360 E= 60 M

196 E =?

= 60*196/360

Weight on Moon is equal to 32.67 pounds

Question 2

	A	B
Annual membership	300	40
List Premium	70%	90%

Let Manufacture price be X

For Plan A

For plan B

Number of Merchandize to purchase to pay same price under both plans, then Plan A must be equal to Plan B

300+0.7X=40+0.9X

300 – 40=0.9X-0.7X

260=0.2X

X=1300

Hence, one must purchase 1,300 units for price of both plans to be equal. At this number of units, for plan A you will pay

300+0.7*1300

=1,210

Similarly for Plan B

40+ 0.9*1300

1,210

Question 3

P=42-0.5X

IF P=5%

Then;

0.05=42-0.5X

0.5X=42-0.05

0.5X=41.95

X=83.9

Hence, after 83.9 years, less than 5% of Americans will be smoking cigarettes. The data is calculated from 1965 onwards.