a. Explanation Given info: The 106 social robots considered for studying the trend of designs of social robots consisted of 63 robots having only legs, 20 having only wheels, 8 having both legs and wheels and 15 having neither legs nor wheels. Out of the 106 social robots, 10 were randomly selected. The number of robots having neither legs nor wheels, among these 10 sampled robots, is denoted by x . Justification: Binomial Distribution: A random variable X is said to follow Binomial distribution if X has only two outcomes “success” and “failure” and the mass function of X is, p ( x ) = ( n x ) p x q n − x , x = 0 , 1 , 2 , ... , n , Where n is the number of trials and p is the probability of success, q = 1 − p . The mean is μ = n p and the standard deviation is σ = ( n p q ) . Requirements for a binomial random variable : The experiment consists of n identical trials. There are only 2 possible outcomes for each trial, success and failure . The probability of success ( S ) remains the same for all trials. The trials are independent of each other. The random variable in the experiment has binomial distribution b. To determine To show: The properties of the hypergeometric probability distribution are satisfied for this experiment. c. To determine To find: The values of μ and σ for the probability distribution of X . d. To determine To calculate: The probability that x = 2 .

Statistics for Business and Economics (13th Edition)

13th Edition

ISBN: 9780134506593

Author: James T. McClave, P. George Benson, Terry Sincich

Publisher: PEARSON

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Chapter 4.4, Problem 4.69ACB

To determine

To demonstrate: The reason of X should not be approximated by the binomial distribution.

To determine

To show: The properties of the hypergeometric probability distribution are satisfied for this experiment.

To determine

To find: The values of μ and σ for the probability distribution of X.

To determine

To calculate: The probability that x=2 .

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Chapter 4.4, Problem 4.68LM

Chapter 4.4, Problem 4.70ACB

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Statistics for Business and Economics (13th Edition)

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To demonstrate: The reason of X should not be approximated by the binomial distribution.

Solution Summary: The author explains that the reason of X should not be approximated by the binomial distribution.

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To demonstrate: The reason of X should not be approximated by the binomial distribution.

To show: The properties of the hypergeometric probability distribution are satisfied for this experiment.

To find: The values of μ and σ for the probability distribution of X.

To calculate: The probability that x=2 .

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Chapter 4 Solutions