Question

Suppose at the shooting range you have a probability of hitting the bullseye on your target of about 10%.

A) What is the probability of hitting the bullseye more than 1 time in 20 shots?

B) What is the mean number of bullseye's you would expect in 20 shots?

C) What is the Standard Deviation of bullseye's you would expect in 20 shots?

Answer 1

Probability of hitting the bullseye : p =10/100 =0.10

Number of shots n : 20

X : Number of times hitting the bullseye

X follows Binomial distribution with n=20 and p=0.10

Probability mass function of X is given by:

Probability of hitting the bullseye 'r' times is given by = P(X=r)

Mean of X = np and standard deviation of X =

A)  probability of hitting the bullseye more than 1 time in 20 shots = P(X>1) = 1-[ P(X=0)+P(X=1)]

P(X>1) = 1-[ P(X=0)+P(X=1)] = 1-[0.12158+0.27017]=1-0.39175=0.60825

Probability of hitting the bullseye more than 1 time in 20 shots = 0.60825

B) Mean number of bullseye's you would expect in 20 shots = np = 20 x 0.10 =2

Mean number of bullseye's you would expect in 20 shots = 2

C) Standard Deviation of bullseye's you would expect in 20 shots =

Standard Deviation of bullseye's you would expect in 20 shots = 1.34164