Solution Found!
Answer: Do social robots walk or roll? Refer to the
Chapter 4, Problem 69E(choose chapter or problem)
Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 4.25 (p.196). The study found that of 106 social robots, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. Suppose you randomly select 10 of the 106 social robots and count the number, \(x\), with neither legs nor wheels.
a. Demonstrate why the probability distribution for \(x\) should not be approximated by the binomial distribution.
b. Show that the properties of the hypergeometric probability distribution are satisfied for this experiment.
c. Find \(\mu\) and \(\sigma\) for the probability distribution for \(x\).
d. Calculate the probability that \(x\) = 2.
Questions & Answers
QUESTION:
Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 4.25 (p.196). The study found that of 106 social robots, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. Suppose you randomly select 10 of the 106 social robots and count the number, \(x\), with neither legs nor wheels.
a. Demonstrate why the probability distribution for \(x\) should not be approximated by the binomial distribution.
b. Show that the properties of the hypergeometric probability distribution are satisfied for this experiment.
c. Find \(\mu\) and \(\sigma\) for the probability distribution for \(x\).
d. Calculate the probability that \(x\) = 2.
ANSWER:Step 1 of 5
Total number of robots = 106.
The number of robots built with legs = 63.
The number of robots built with wheels = 20.
The number of robots built with both legs and wheels = 8.
The number of robots built with neither legs nor wheels = 15.
Here our goal is:
a). We need to demonstrate the probability distribution for x should not be approximated by the binomial distribution.
b). We need to show that the properties of the hypergeometric probability distribution are satisfied for this experiment.
c). We need to find ? and ? for the probability distribution for x.
d). We need to calculate the probability that x = 2.