Question

Every 5 out 8 people pass their driver's license tests on the first attempt. You surveyed 100 people who have just finished their tests. What is the probability that more than 65 people passed on their first trial (round your number to 3 decimal places)?    

Answer 1

Given,

Every 5 out 8 people pass their driver's license tests on the first attempt.

Probability of pass their driver's license tests at first attempt =5/8 =0.625

Number of people just finished their tests : n=100

X: Number of people pass their driver's license tests on the first attempt.

We want to find the probability of more than 65 people passed on their first trial = P(X > 65)

For the given scenario X~ Binomial distribution with n=100 and p = 0.625

Therefore,

P(X>65) = 1 – P (X ≤ 65)

Cumulative distribution unction to obtain the probability is as below.

After solving the above equation

P (X≤65) = 0.7304

Therefore,

P(X>65) = 1 – 0.7304 = 0.2696 = ~ 0.27

Probability of more than 65 people passed on their first trial = ~ 0.27