Question

About 85% of people who take the G1 driving test pass on their first try. If 205 applicants try the test, what is the probability that more than 25 need to retake the test?

Please explain using binomial distribution

Answer 1

P( passing the test on their first try) = 0.85

Let X be the number of applicants pass the test on their first try

X~ N( 205, 0.85)

As X is quite large , we will use normal approximation

X~ N( np, np(1-p))

~ N( 174.25, 26.1375)

P( more than 25 need to retake the test) = P( less than180 pass the test )

= P( X < 180)

= P( <   )

= P( Z < 1.12)

=0.86864

OR

P( more than 25 need to retake the test) = P( less than 180 pass the test)

= 0.86864