Question

From driverless cars to a workplace staffed by robots, automation has the potential to reshape many facets of American life. The large majority of Americans (87%) would favor a requirement that all driverless vehicles have a human in the driver's seat who can take control of the vehicle in the event of an emergency, while 56% of U.S. adults say that they would not ride in a driverless vehicle.† If these figures are correct, what is the probability that in a sample of

n = 100

U.S. adults, the sample proportion p̂ of adults who would not ride in a driverless vehicle falls between 52% and 62%? (Round your answer to four decimal places.)

Answer 1

Solution

Given that,

p = 0.56

1 - p = 1 - 0.56 = 0.44

n = 100

= p = 0.56

=  [p ( 1 - p ) / n] = [(0.56 * 0.44 ) / 100 ] = 0.0496

P(0.52 < < 0.62 )

= P[(0.52 - 0.56) / 0.0496 < ( - ) / < (0.62 - 0.56) / 0.0496]

= P(-0.81 < z < 1.21)

= P(z < 1.21) - P(z < -0.81)

Using z table,   

= 0.8869 - 0.2090

= 0.6779