a. To determine Find the mean and the standard deviation of the number of heads. Explanation Calculation: A coin was tossed 36 times. Properties of Bernoulli trials: In each trial there will be only two possible outcomes, success and failure. The probability of success for each trial is same. Each trial is independent to each other. 10% condition for Bernoulli trials: If the sample size is less than 10% of the population size, then is can be said that the Bernoulli trials must be independent. Binomial probability for Bernoulli trials: The number of successes in a specified number of Bernoulli trials is described by Binomial model. If the number of trials is n , with the probability of success is p and the probability of failure is q = 1 − p , and X be the event of the number of success in n independent trials, then the binomial probability model is defined as, P ( X = x ) = C n x p x q n − x , C n x = n ! x ! ( n − x ) ! and x = 0 , 1... n With mean is μ = n p and standard deviation is σ = n p q b. To determine Find the number of extra heads for unusual results. c. To determine Explain whether for 100 number tosses, the same number of heads will be unusual or not. d. To determine Find the number of extra heads which will be unusual for 100 tosses. e. To determine Explain how the results refute the law of averages but confirms the law of large numbers.

4th Edition

ISBN: 9780321825278

Author: Richard D. De Veaux, Paul F. Velleman, David E. Bock

Publisher: PEARSON

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Chapter R, Problem 4.40RE

To determine

Find the mean and the standard deviation of the number of heads.

To determine

Find the number of extra heads for unusual results.

To determine

Explain whether for 100 number tosses, the same number of heads will be unusual or not.

To determine

Find the number of extra heads which will be unusual for 100 tosses.

To determine

Explain how the results refute the law of averages but confirms the law of large numbers.

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Chapter R, Problem 4.39RE

Chapter R, Problem 4.41RE

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