The probability of a radar station detecting an enemy plane is 0.85. If 7 stations are in use, what is the standard deviation? Round your answer to nearest hundredth.
A)2.44
B)0.94
C)0.89
D)5.95
E)none of these choices

Question

Quizplus · Accepted Answer

The number of successful detections (X) follows a binomial distribution with parameters n=7 and p=0.85.

The mean of X is given by: 
μ = np = 7(0.85) = 5.95

The variance of X is given by: 
σ^2 = np(1-p) = 7(0.85)(1-0.85) = 0.8925

The standard deviation is the square root of the variance: 
σ = sqrt(0.8925) ≈ 0.94 (rounded to nearest hundredth)

Therefore, the answer is B) 0.94.

The Probability of a Radar Station Detecting an Enemy Plane