Question

Approximately 85% of applicants get their G1 drivers license the first time trying the test. if 80 applicants take the test, what is the probability more than 10 applicants will have to retake the test. Use normal approximation to binomial distribution

Answer 1

so we want
P( X >= 10 )

Answer 2

the probability of passing the test the first time is .85.
the probability of having to retake the test is 1-.85

Answer 3

ie failing the test

Answer 4

is 0.15

Answer 5

right :)

Answer 6

how would I get the z-score?

Answer 7

you would have to use a binomial continuity correction , as well

Answer 8

The mean of the binomial distribution is \(np\), where \(n\) is the number of trials and \(p\) is probability of success.

Answer 9

so 10.5?

Answer 10

80*.15 = 12

Answer 11

While the standard deviation is given by \(\sqrt{npq}\) where \(q=1-p\) or probability of failure.

Answer 12

teh standard deviation is sqrt( n * p * (1-p))

Answer 13

the*

Answer 14

when finding the mean, np, is p .85 or .15

Answer 15

So our z score will be: \[
z = \frac{x-np}{\sqrt{np(1-p)}}
\]where \(x\) is the number of success we want

Answer 16

In our case, success would mean that you have to retake the test, ironically

Answer 17

You are going to want P( X >= 9.5) because you are approximating a discrete distribution with a continuous one.
alternatively you can also solve this problem with a complement

Answer 18

okay I got it, thank you :)

Answer 19

1/8 as a fraction it would be 1 out of 8 i believe i don't know much i'm only in the seventh grade