The probability that an amateur archer hits a target 50 feet

The probability that an amateur archer hits a target 50 feet away is 20%. Suppose we take a sample of 50 archers.

1. What is the standard error of the proportion?

2. What is the probability that the proportion of archers who hit the target will be greater than 35%?

Solution

1.) standard error = sqrt(p*(1-p)/n) = sqrt(0.2*0.8/50) = 0.05657

2.) Mean = 0.2

standard error = 0.05657

P(X>35%) = P(X>0.35) = P(Z>(0.35-0.2)/0.05657) = P(Z>2.65) = 1 - 0.9960 = 0.004