Question

A survey team from the Department of Statistics and Actuarial Science, UG have established that 15% of cars in Accra are known to have faulty brake lights. Determine the probability that, in a random sample of 50 cars, more than 5 cars but fewer than 10 cars have faulty brake lights.

A. 0.572
B. 0.432
C. 0.136
D. 0.057

Answer 1

1. Calculate the probability of having exactly 5
cars with faulty brake lights: P(X = 5) = (50
choose 5) * (0.15)^5 * (0.85)^(50-5)

2. Calculate the probability of having exactly 10
cars with faulty brake lights: P(X = 10) = (50
choose 10) * (0.15)^10 * (0.85) ^(50-10)

3. Calculate the cumulative probability of having more than 5 cars but fewer than 10 cars: P(5 < X
< 10) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)

4. Add up the individual probabilities calculated in step 3 to get the final probability.

By doing this, we find that the answer is approximately 0.432. Therefore, the correct option is B. 0.432.