Question

Suppose 75% of drivers rate themselves "good" drivers. Suppose 20 drivers are randomly selected. Find the probability that between 14 and 16 drivers, inclusive, rate themselves as a "good" driver. Note: you must state the probability distribution and/or formulas.

Answer 1

We are given n = 20 , p = 0.75

Here n*p = 15 > 5 and n*(1-p) = 5 5

So we can use normal approximation

We asked P( 14 X 16)

P(14X 16) = P [ 14-0.5 < X < 16 +0.5]

= P[13.5 < X < 16.5]

= P[ 13.5-n*p/sqrt [n*p*q] < X -n*p/sqrt[n*p*q] < 16.5-n*p/sqrt[n*p*q] ]

= P [ (13.5-15)/1.94 < Z < (16.5 - 15)/1.94]

= P( -0.77 < Z < 0.77)

P( 14 X 16) = P( Z < 0.77) - P( Z < -0.77)

= 0.7794 - 0.2206

P( 14 X 16 ) = 0.5588