At an airport, 83% of recent flights have arrived on time. A sample of 12 flights is studied. What is the standard deviation of the number of flights that are on time?
A) 1.69
B) 9.96
C) 1.30
D) 0.38

Question

Quizplus · Accepted Answer

The standard deviation of a binomial distribution can be calculated using the formula σ = sqrt(npq), where n is the number of trials, p is the probability of success, and q is the probability of failure (q = 1 - p). 
In this case, n = 12 and p = 0.83 (since 83% of recent flights have arrived on time, the probability of success is 0.83). Therefore, q = 1 - 0.83 = 0.17. 
Using the formula, we get: 
σ = sqrt(12 x 0.83 x 0.17) ≈ 1.30 
Therefore, the standard deviation of the number of flights that are on time is approximately 1.30, which corresponds to choice C.

At an Airport, 83% of Recent Flights Have Arrived on Time