In: Statistics and Probability
1. A magazine reported that 10% of American drivers read the newspaper while driving. If 500 drivers are selected at random, find the probability that exactly 50 will admit to reading the newspaper while driving.
Mean ( X ) = n * P = 500 * 0.10 = 50
Standard deviation ( X ) =
Using Normal Approximation to Binomial
P ( X = 50 ) Using continuity correction
P ( 50 - 0.5 < X < 50 + 0.5 ) = P ( 49.5 < X < 50.5 )
P ( 49.5 < X < 50.5 )
Standardizing the value
Z = ( 49.5 - 50 ) /
6.7082
Z =
-0.07
Z = ( 50.5 - 50 ) /
6.7082
Z =
0.07
P ( -0.07 < Z < 0.07 )
P ( 49.5 < X < 50.5 ) = P ( Z < 0.07 ) - P ( Z < -0.07
)
P ( 49.5 < X < 50.5 ) = 0.5297 -
0.4703
P ( 49.5 < X < 50.5 ) =
0.0594
P ( X = 50 ) = 0.0594