Lee Iacocca volunteered to drive one of his Chryslers into a brick wall to demonstrate the effectiveness of airbags used in these cars. Airbags are known to activate at random when the car decelerates anywhere from 9 to 14 miles per hour per second (mph/s). The probability distribution for the deceleration speed at which bags activate is given below.
|
mph/s
|
Probability
|
|
9
|
0.12
|
|
10
|
0.23
|
|
11
|
0.34
|
|
12
|
0.21
|
|
13
|
0.06
|
|
14
|
0.04
|
a. If the airbag activates at a deceleration of 12 mph/s or more, Iacocca would get hurt. What is the probability of his being hurt in this demonstration?
b. What is the mean deceleration at airbag activation moment?
c. What is the standard deviation of deceleration at airbag activation time?