MATH221 Week 4.2017 Lab Your Name Here Times New Roma 12 B 1 U A.. Statistics-La
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Question
MATH221 Week 4.2017 Lab Your Name Here Times New Roma 12 B 1 U A.. Statistics-Lab -Week 4 MATH221 Statistical Concepts: Probability Binomial Probability Distribution Recall that there are two approaches to probability that wecovered chapter 3. One being the theoretical (classical) approach, which gives us exact probabilities for events based on the elements ofthe sample space having an equal likelihood of occurrence. The other is the empirical (statistical) approach, in which probabilities are found by experimentation. In this lab we will explore the binomial distribution a bit closer by comparing the theoretical probabilities to those found by experimentation. The procedure: Flipping a fair coin 12 times. A success: A tail occurs Check Binomial Requirements: 1. Check the requirements of the binomial distribution for this experiment. Be specific with the requirements with respect to the given procedure. Requirements Trials are independent or dependent? (Circle one) Does p remain constant? Yes or No (Circle One) 4. x mExplanation / Answer
1. Requirements :-
1. n=12 ; Trials are independent.
2. S=Tails ; F=Heads
3. p=probability of success=1/2 ; Yes, p remain constant for each trial.
4. x=number of success= 0(1)12
2.
3. For sample of size 20,
Mean=5.35 ; Variance=2.6275 ; s.d.=1.621
4. n=12, p=0.5
5. Mean = np=12×0.5=6.00 ; Variance=np(1-p)=12×0.5×(1-0.5)=3.00 ; s.d.=(Variance)=(3.00)=1.732
6. In part 3 mean was 5.35 and part 5 mean is 6.00 ie.. they are close, if sample size (20) increases it converges to 6.00
Similarly, in part 3 mean was 1.621 and in part 5 it is 1.732 ie.. they are too close. In this case also, if sample size increases the sample mean will converges to Population Mean (1.732)
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Experiment 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 No of Tails 4 6 6 7 8 5 8 6 7 6 3 3 4 5 7 5 2 4 5 6Related Questions
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