11 Statistics & Prob Learning Activity Sheet Quarter 3 PDF

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STATISTICS andPROBABILITYThird QuarterLEARNING ACTIVITY SHEETS11iiRepublic of the Philippines Department of Education REGION II – CAGAYAN VALLEYCOPYRIGHT PAGE Learning Activity Sheet in Statistics and Probability Grade 11 Copyright @ 2020 DEPARTMENT OF EDUCATION Regional Office No. 02 (Cagayan Valle...

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11 STATISTICS and PROBABILITY Third Quarter

LEARNING ACTIVITY SHEETS

Republic of the Philippines

Department of Education REGION II – CAGAYAN VALLEY

COPYRIGHT PAGE Learning Activity Sheet in Statistics and Probability Grade 11 Copyright @ 2020 DEPARTMENT OF EDUCATION Regional Office No. 02 (Cagayan Valley) Regional Government Center, Carig Sur, Tuguegarao City, 3500 “No copy of this material shall subsist in any work of the government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. This material has been developed for the implementation of K to 12 Curriculum through the Curriculum and Learning Management Division (CLMD). It can be reproduced for educational purposes and the source must be acknowledged. Derivatives of the work including creating an edited version and enhancement of supplementary work are permitted provided all original works are acknowledged and the copyright is attributed. No work may be derived from the material for commercial purpose and profit. Consultants: Regional Director : BENJAMIN D. PARAGAS, PhD, IV Assistant Regional Director : JESSIE L. AMIN, EdD, CESO V Schools Division Superintendent : MADELYN L. MACALLING, PhD, CESO VI Assistant Schools Division Superintendents : DANTE MARCELO, PhD, CESO VI : EDNA P. ABUAN, PhD Chief Education Supervisor, CLMD : OCTAVIO V. CABASAG, PhD Chief Education Supervisor, CID : RODRIGO V. PASCUA, EdD Development Team Writers

: ALJON S. BUCU, PhD, REGIONAL SCIENCE HS- ISABELA : JAYBEL B. CALUMPIT, REGIONAL SCIENCE HS- ISABELA : LEONOR BALICAO, DELFIN ALBANO STAND ALONE SHS-ISABELA

Content Editor

: ALJON S. BUCU, PhD : MAI RANI ZIPAGAN, PhD : LEONOR BALICAO : CORAZON A. BAUTISTA

Focal Persons

: INOCENCIO T. BALAG, EPS MATHEMATICS

: MA. CRISTINA ACOSTA, EPS LRMDS, SDO ISABELA : ISAGANI R. DURUIN, PhD, REGIONAL EPS MATHEMATICS : RIZALINO G. CARONAN, REGIONAL EPS LRMDS Printed in DepEd Regional Office No. 02 Regional Government Center, Carig Sur, Tuguegarao City

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Table of Contents Competencies

Page Number

Illustrate a random variable (discrete and continuous) and distinguish between a discrete and a continuous random variable Find the possible values of a random variable and illustrate a probability distribution for a discrete random variable and its properties Compute the Probabilities Corresponding to a Given Random Variable Illustrate the Mean and Variance of a Discrete Random Variable Calculate the Mean and Variance of a Discrete Random Variable Interpret the mean and variance of a discrete random variable Solve problems involving mean and variance of probability distributions Illustrate a normal random variable and its characteristics Identify region under the normal curve corresponding to different standard normal values Convert a random variable to a standard normal variable and vice versa Compute probabilities and percentiles using the standard normal table Illustrate the different random sampling methods Distinguish between parameter and statistic Identify sampling distributions of statistics (sample mean) Find the mean and variance of the sampling distribution of the sample means and define the sampling distribution of the sample mean for normal population when the variance is: a) known; b) unknown Illustrate the central limit theorem Defines the sampling distribution of the sample mean using the Central Limit Theorem Solve problems involving sampling distributions of the sample mean Illustrate the t-distribution Identify the percentiles using the t-distribution table Identify the length of a confidence interval Compute for the length of a confidence interval Compute for an appropriate sample size using the length of a confidence interval Solve problems involving sample size determination

1

5 10 14 25 33 42 50 56 64 70 75 80 84 89

102 109 117 126 132 142 150 155

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STATISTICS & PROBABILITY 11 Name: ________________________________ Date: _________________________________

Grade Level: _______ Score: _____________

LEARNING ACTIVITY SHEET RANDOM VARIABLES Background Information for Learners

A random variable X is a variable that assumes numerical values associated with the random outcomes of an experiment, where one (and only one) numerical value is assigned to each sample point. Random variables are denoted by uppercase letters and particular values of the variable are denoted by lower case letters. A discrete random variable is one that can assume a countable number of values. Mostly, discrete random variables represent count data, such as number of students in a class. These data assume only countable number of values. A continuous random variable takes on values on a continuous scale. Often, continuous random variables represent measured data, such as heights and weights. The possible values are uncountably infinite.

Example Suppose two coins are tossed. Let Z be the random variable representing the number of heads that occur. Find the values of the random variable Z. Value of the Random Variable Z (number of heads) HH 2 HT 1 TH 1 TT 0 So, the possible values of the random variable Z are 0, 1, and 2. Possible Outcomes

1

Learning Competency with code The learner is able to illustrate a random variable (discrete and continuous) and distinguish between a discrete and a continuous random variable (M11/12SP-IIIA-1-2) Directions/Instructions: A. Find the possible values of the random variable described in each situation. 1. Two balls are drawn in succession without replacement from an urn containing 4 red balls and 5 blue balls. Let R be the random variable representing the number of red balls. Find the values of the random variable R. 2. In a hospital, a statistician records the sex of newborn babies. Let M be the random variable representing males among five newborn babies. 3. Let Z be a random variable representing the result of rolling a die. 4. Four coins are tossed. Let T be the random variable representing the number of tails that occur. Find the values of the random variable T. 5. From a box containing 4 black balls and 2 green balls, 3 balls are drawn in succession. Each ball is placed back in the box before the next draw is made. Let G be a random variable representing the number of green balls that occur. Find the values of the random variable G. B. Classify the following random variables as discrete or continuous. 1. The number of people infected by COVID-19 in the Philippines 2. The number of text messages sent in a day 3. The time (in hours) needed to finish this activity 4. The body temperature of sick person 5. The volume of milk consumed by an infant in a day 6. The number of gadgets sold by a mobile company in a week 7. The number of grafted mango seedlings sold in a month 8. The amount of ink used in printing promotional posters 9. The number of medical front liners in a hospital 10. The distance travelled by a car using 10 liters of gasoline 11. The time consumed on Facebook by an online seller in a day 12. The number of people helping the church every Sunday 13. The volume of water needed by an indoor plant in order to survive in a month 14. The length of time in minutes that a scheduled airplane flight is delayed 15. The number of aircraft near-collisions observed by an air controller over a 24-hour period

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C. Choose the letter that corresponds to the correct answer. 1. Which of the following is a discrete random variable? a. The stained area of the floor when a glass of coffee spills on it b. The time in seconds that a runner completes a 200-meter race c. The exact mass of a buko pie made by a baker d. The number of customers each day in computer shop 2. Which of the following is NOT a true statement? a. b. c. d.

Random variables can only have one value. The value of a random variable could be zero. A random variable cannot be negative. A random variable can be discrete or continuous.

3. Three coins are tossed at once, which are possible values of the random variable for the number of coins that match? a. {0,1} b. {1,2} c. {2,3} d. {3} 4. You decide to conduct a survey of families with two children. You are interested in counting the number of girls (out of 2 children) in each family. Is this a random variable, and if it is, what are all its possible values? a. yes, it is a random variable, and its values can be 1 or 2 b. yes, it is a random variable, and its values can be 0, 1 or 2 c. yes, it is a random variable, and its values can be 2 or 4 d. No, it is not a random variable, since it is not random 5. Which of the following is a continuous random variable? a. The number of eggs that a hen lay in a day b. The number of people watching an Inter-town basketball game c. The average weight of male athletes d. The amount of paint used in painting clay pots

Reflection

Complete this statement: What I learned in this activity ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

3

References: Avillano-Tales, Karen. Senior High School Statistics and Probability.FNB Educational, Inc. 2016 Belecina, R.R., Baccay, E.S., & Mateo E.B. Statistics & Probability. Rex Book Store.2016 Chua, S.L., Dela Cruz, E Jr O., Aguilar, I.C., Rodriguez, A.A.& Puro, L.M. Soaring 21st Century Mathematics (Statistics & Probability).Phoenix Publishing House, Inc.2016

Answer Key

A. 1. 0, 1, and 2 2. 0, 1, 2, 3, 4 and 5 3. 0, 1, 2, 3, 4, 5 and 6 4. 0, 1, 2, 3 and 4 5. 0, 1and 2 B. 1. discrete 2. discrete 3. discrete 4. continuous 5. continuous 6. discrete 7. discrete 8. continuous 9. discrete 10. continuous 11. continuous 12. discrete 13. continuous 14. continuous 15. discrete C. 1. d 2. a 3. c

4. b 5. c 4

STATISTICS & PROBABILITY 11 Name: ________________________________ Date: _________________________________

Grade Level: _______ Score: _____________

LEARNING ACTIVITY SHEET DISCRETE PROBABILITY DISTRIBUTIONS Background Information for Learners

The probability distribution of a discrete random variable X shows the probabilities associated with all possible outcomes. It may be expressed in tabular, formula and graphical form. Properties of a Probability Distribution 1. The probability of each value x is a value between 0 and 1, or equivalently, 0 ≤ 𝑃(𝑋) ≤ 1. 2. The sum of the probabilities of the values equals 1. ∑ 𝑃 (𝑋) = 1 Example Suppose three cell phones are tested at random in preparation for the online class. Let D represent the defective cell phone and let N represent the non-defective ones. If we let X be the random variable for the number of defective cell phones, construct the probability distribution in tabular and formula form then draw the corresponding probability histogram.

Solution Determine the sample space and count the number of defective cell phones in each outcome. Value of the Random Variable X (number of defective cell phones) NNN 0 NND 1 NDN 1 DNN 1 NDD 2 DND 2 DDN 2 DDD 3 There are four possible values of the random variable X (0, 1, 2 and 3). Possible outcomes

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a. Tabular form of the probability distribution Number of Defective Cell phones X Probability P(X)

0

1

2

3

1 8

3 8

3 8

1 8

b. Formula form of the probability distribution 1 𝑖𝑓 𝑋 = 0,3 8 ( ) 𝑃 𝑋 ={ 3 𝑖𝑓 𝑋 = 1, 2 8

Probability P(X)

c. The graph shows the probability histogram of the distribution 0.400 0.350 0.300 0.250 0.200 0.150 0.100 0.050 0.000 0

1

2

3

Number of Defective Cell Phones

Learning Competency with code The learner is able to find the possible values of a random variable and illustrate a probability distribution for a discrete random variable and its properties (M11/12SP-IIIA-3-4)

Directions/Instructions: D. Construct a probability distribution in tabular form for the random variable described in each situation. 1. Suppose three coins are tossed. Let Y be the random variable representing the number of tails that occur. 6

2. A shipment five computers contains two that are slightly defective. A retailer receives three of these computers at random. Let Z represent the number of computers purchased by the retailer which are slightly defective.

3. Make a probability distribution table for the numbers on the spinning wheel. Let X be the number on the wheel.

1

3

2 3

3 3 1 3

E. Determine whether the distribution represents a probability distribution for a discrete random variable. 1 1 3

5 1 3

3 0.10

X P (X)

7 1 3

8 1 3

9 1 3

3

2

1

0

0.30

0.40

0.10

0.10

1.

2. X P (X)

3. X P (X) 4. X P (X)

0 1 6

1 5 18 0 0.15

2 2 9 1 0.35

3 1 6 2 0.52

4 1 9 3 0.78

5 1 18 4 0.84

7

5. X

10

15

20

25

30

P (X)

- 0.05

0.25

0.3

0.4

0.10

C. For each of the following, determine whether it can serve as the probability distribution of a random variable X. 1. P (X) = 2. P (X) = 3. P (X) = 4. P (X) = 5. P (X) = Reflection

𝑋 for X = 1, 2, 3 6

1

8

for X = 1, 2 3,…, 8

1+𝑋

1−𝑋 12

25𝑋

𝑋−3 7

for X = 1, 2, 3, 4 for X = 1, 2, 3, 4 for X = 1, 2, 3, 4, 5

Complete this statement. What I learned in this activity ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

References: Avillano-Tales, Karen. Senior High School Statistics and Probability.FNB Educational, Inc. 2016 Belecina, R.R., Baccay, E.S., & Mateo E.B. Statistics & Probability. Rex Book Store.2016 Chua, S.L., Dela Cruz, E Jr O., Aguilar, I.C., Rodriguez, A.A.& Puro, L.M. Soaring 21st Century Mathematics (Statistics & Probability).Phoenix Publishing House, Inc.2016

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Answer Key A. 1.

Number of Tails Y 0 1 2 3

2.

Number of Slightly Defective Computers Z 0 1 2

3. Number on the Wheel X 1 2 3 B. 1. No 2. Yes 3. Yes 4. No 5. No

C. 1. Yes 2. Yes 3. No 4. Yes 5. No

Probability P(Y) 1 8 3 8 3 8 1 8 Probability P(Z) 1 7 3 7 3 7 Probability P(X) 1 4 1 8 5 8

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STATISTICS AND PROBABILITY Name of Learner:________________

Grade Level:______

Section:________________________

Date:____________

LEARNING ACTIVITY SHEET THE PROBABILITIES CORRESPONDING TO A GIVEN RANDOM VARIABLE

Background Information for Learners In your previous lessons, you have learned to find the possible values of a random variable. This time you will learn how to compute probabilities that correspond to a given random variable. Probability of an Event The probability of an event, denoted as P(X), is the numerical measure of the likelihood that an event will occur. It is calculated by finding the quotient of the number of favorable outcomes and the total number of possible outcomes, In symbols, 𝑛 (𝑋)

P(X)= 𝑛 (𝑆)

where n(X) is the number of the elements in the event and n(S) is the number of the elements in the sample space. Example 1. Suppose two coins are tossed. If X is a random variable representing the number of tails that occur, find the probability that 1 head will come out. will come out P(1) is 4 = or 50% or P(X)= 𝑛 (𝑆)= 4= 𝑜𝑟 50%. 2 2

1

𝑛(𝑋)

2 1

Solution. The possible outcomes are HH,HT,TH and TT. Therefore, the probability that 1 head 2

Example 2. Kenneth had thrown a pair of dice. What is the probability of getting a sum of 6? 9? Solution: The sample space is the set {(2,4) (4,2), (3,3), (5,1), (1,5)} and there are 36 elements in the sample space. Hence, the probability of getting a sum of 6 is P(X)=

𝑛 (𝑋 )

𝑛 (𝑆)

= 36 𝑜𝑟 13.89% 5

P(X)= 𝑛 (𝑆) = 36 𝑜𝑟 11.11% 𝑛 (𝑋 )

4

while the probability of getting a sum of 9 is

10

Example 3. Suppose a card is selected at random from a deck of 52 cards. Compute for the probability of picking a “red queen” at random. Solution: The event “red queen” has two elements: E= { queen of spades, queen of clubs}. Since there are 52 cards, the probability of picking a red queen is P(X)= 𝑛 (𝑆) = 52 = 𝑛 (𝑋 )

2

1 26

or 3.85%

The Complement Rule of Probability The probability that an event will happen P(E) and the probability that it will not happen P(E’) give a sum of 1, or in symbols, P(E) + P(E’)=1. Therefore, P(E’)=1-P(E). Example 5. Maria, a Grade 11 student has a bag with 4 blue, 6 red and 10 yellow balloons. What is the probability that a balloon chosen at random is not yellow? 10

= 2 𝑜𝑟 50%. Using the complement rule, the probability that the balloon chosen is not yellow 1

Solution: Since there are 10 yellow balloons in a bag, the probability of getting a yellow balloon is

20

is:

P(not yellow)= 1- P(yellow), hence, 1 P(not yellow)= 1- 2 or 50% Learning Competency The learner is able to compute the Probabilities Corresponding to a Given Random Variable (M11/12SP-111a-6)

EXERCISE 1 Directions: Determine whether the following value can represent a probability. Show your solutions and explain you answer. , ,

1 1

1

,

1

, , and 1

2 6 12 12 12

,respectively. 2. The probabilities that doctors save 5,6,7,8 or 9 covid-19 patients in one day are 0.18, 0.25, 0.1, 0.3 and 0.17 respectively 3. The probabilities that a businessman will invest P 28,000, P 50,000, or P 75,000 are 1 1 1 , , 𝑎𝑛𝑑 . 1. The probabilities that a bias die will fall as 1,2,3,4,5, and 6 are 1

12

5 5

1

5

10

5

15

4. P(1)= 19, P(2)= 19, P(3)= 19, P(4)= 19 5. P(1)= 0.1, P(2)= 0.2, P(3)= 0.3, P(4)= 0.4,

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EXERCISE 2 Directions: Answer the following problems using the Complement Rule of probability. 1. Ma. Laarni had a box containing 8 white balls, 6 green balls and 4 red balls which she uses for her experiment. If a ball is chosen at random, what is the probability that a. it is not white? b. It is not green? c. It is not red? 2. Kyla Mae and Mary Joy are two Senior High School students running for a position in the Student Supreme Government. If the probability that Kyla Mae will win the election is 0.52, What is the probability that Mary Joy will win? 3. Jomarson has three coins and tossed it simultaneously. Find the probability of showing at least one head.

EXERCISE 3 Directions: Answer the following problems with accuracy. Show your complete solutions. 1. In a Statistics and Probability class, Kenjie was assigned to draw from an ordinary ...