Question

The probability that Sergeant Fernandez hits its target each time he shoots is 0.6. Suppose that Sergeant Mendez shoots at a target 20 times.

a. Argue that this is a binomial experiment.

b. Find the probability he hits the target 3 times.

c. What is the probability he hits his target at least 7 times?

d. What is the expected number of shots that hit the target.

e. What is the standard deviation of the number of shots that hit the target.

Answer 1

Part a)

X ~ B ( n = 20 , P = 0.6 )

Since trials are independet, probability of success is 0.6, hence it is binomial experiment.

Part b)

Part c)

P(X = 0 ) = 0
P(X = 1 ) = 0
P(X = 2 ) = 0
P(X = 3 ) = 0
P(X = 4 ) = 0.0003
P(X = 5 ) = 0.0013
P(X = 6 ) = 0.0049

P ( X >= 7 ) = 1 - P ( X < 7 ) = 1 - 0.0065 = 0.9935

Part d)

Mean = n * P = ( 20 * 0.6 ) = 12

Part e)

Variance = n * P * Q = ( 20 * 0.6 * 0.4 ) = 4.8
Standard deviation = √(variance) = (4.8) = 2.1909