Explanation Given: A coin is biased so that the probability of it landing heads is 0.6 and the coin is tossed 100 times. Approach: The mean for the binomial random variable X is given as, μ = n p → ( 1 ) Here, n is the number of trials and p is the probability of success. The standard deviation for the binomial random variable X is given as, σ = n p q → ( 2 ) Here, q is the probability of failure. In normal distribution with mean μ and standard deviation σ , the probability of random variable X is given as, P ( X > x ) = P ( Z > x − μ σ ) → ( 3 ) Calculation: The probability that biased coin will land heads is, p = 0.6 The probability that biased coin will land tails is, q = 1 − p = 1 − 0.6 = 0.4 Substitute 100 for n and 0.6 for p in equation ( 1 ) , to calculate the mean. μ = ( 100 ) ( 0.6 ) = 60 Therefore, the mean of the number of heads is 60

12th Edition

ISBN: 9780357308615

Author: Tan

Publisher: CENGAGE L

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Chapter 8.CRE, Problem 31CRE

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The probability that heads will appear more than 50 times in the 100 tosses.

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Chapter 8.CRE, Problem 30CRE

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The probability that heads will appear more than 50 times in the 100 tosses.

Solution Summary: The author calculates the probability that a coin will land heads more than 50 times in the 100 tosses of the biased coin.

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The probability that heads will appear more than 50 times in the 100 tosses.

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