Solution Found!
Do social robots walk or roll? Refer to the
Chapter 4, Problem 25E(choose chapter or problem)
Problem 25E
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 2.3 (p. 48).
Recall that in a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. Assume the following: Of the 63 robots with legs only, 50 have two legs, 5 have three legs, and 8 have four legs; of the 8 robots with both legs and wheels, all 8 have two legs. Suppose one of the 106 social robots is randomly selected. Let x equal the number of legs on the robot.
a. List the possible values of x.
b. Find the probability distribution of x.
c. Find E(x) and give a practical interpretation of its value.
2.3 Do social robots walk or roll? According to the United Nations, social robots now outnumber industrial robots worldwide. A social (or service) robot is designed to entertain, educate, and care for human users. In a paper published by the International Conference on Social Robotics (Vol. 6414, 2010), design engineers investigated the trend in the design of social robots. Using a random sample of 106 social robots obtained through a Web search, the engineers found that 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. This information is portrayed in the accompanying graph.
a. What type of graph is used to describe the data?
b. Indentify the variable measured for each of the 106 robot designs.
c. Use the graph to identify the social robot design that is currently used the most.
d. Compute class relative frequencies for the different categories shown in the graph.
e. Use the results from, part d to construct a Pareto diagram for the data.
Questions & Answers
QUESTION:
Problem 25E
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 2.3 (p. 48).
Recall that in a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. Assume the following: Of the 63 robots with legs only, 50 have two legs, 5 have three legs, and 8 have four legs; of the 8 robots with both legs and wheels, all 8 have two legs. Suppose one of the 106 social robots is randomly selected. Let x equal the number of legs on the robot.
a. List the possible values of x.
b. Find the probability distribution of x.
c. Find E(x) and give a practical interpretation of its value.
2.3 Do social robots walk or roll? According to the United Nations, social robots now outnumber industrial robots worldwide. A social (or service) robot is designed to entertain, educate, and care for human users. In a paper published by the International Conference on Social Robotics (Vol. 6414, 2010), design engineers investigated the trend in the design of social robots. Using a random sample of 106 social robots obtained through a Web search, the engineers found that 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. This information is portrayed in the accompanying graph.
a. What type of graph is used to describe the data?
b. Indentify the variable measured for each of the 106 robot designs.
c. Use the graph to identify the social robot design that is currently used the most.
d. Compute class relative frequencies for the different categories shown in the graph.
e. Use the results from, part d to construct a Pareto diagram for the data.
ANSWER:
Answer
Step 1 of 3
(a)
We have given a random sample of social robots. Where 63 were built with legs, 20 with wheels, 8 with both legs and wheels, and 15 with neither legs nor wheels.
Assume the following: of the 63 robots with legs only, 50 have two legs, 5 have three legs, and 8 have 4 legs; of the 8 robots with both legs and wheels, all 8 have two legs.
Suppose one of the 106 social robots is randomly selected.
Let equal the number of legs on the robot.
We are asked to list the possible values of
Since we have given out of 106 robots, there are possible combinations of no legs, two legs, three legs, and four legs.
The possible value of is,
Hence the possible value of is