A population has a proportion equal to 0.30.Calculate the following probabilities with n = 100.Find P( ≤ 0.35).
A)0.7244
B)0.8621
C)0.7124
D)0.6126

Question

A population has a proportion equal to 0.30.Calculate the following probabilities with n = 100.Find P(  ≤ 0.35).
A)0.7244 
B)0.8621 
C)0.7124 
D)0.6126

Quizplus · Accepted Answer

We can use the normal approximation to the binomial distribution:
mean = np = 100 x 0.3 = 30
standard deviation = sqrt(npq) = sqrt(100 x 0.3 x 0.7) = 4.58
z-score = (0.35 - 0.3) / 0.458 = 1.09
Using a standard normal table or a calculator, we find the probability to be approximately 0.8621. Therefore, the best choice is (B).

A Population Has a Proportion Equal to 0