Question

Through extensive testing, a weapons manufacturer has determined that their missiles success-

fully hit moving targets with probability 0.56. Suppose that eight missiles are (independently)

Öred, one at each of eight moving targets.

a).What is the probability that the number of targets hit is within 1 standard

deviation of its mean value?

Answer 1

Suppose X is the number of targets hit in 8 independent missiles.

Here X ~ bin(8, 0.56)

So, mean = E(X) = 8*0.56 = 4.48.

Standard deviation = sd(X) = = 1.9712.

So, we have to determine,

P[4.48 - 1.9712 < X < 4.48 + 1.9712]

= P[2.5088 < X < 6.4512]

= P[X < 6.4512] - P[X < 2.5088]

= 0.9295345 - 0.07942471 [The less than type probabilities calculated by R codes pbinom(6.4512,8,0.56) and pbinom(2.5088,8,0.56)]

= 0.8501098.