The normal distribution can be used to approximate the sampl

The normal distribution can be used to approximate the sampling distribution of the sample proportion with a probability of success 0.86 if the sample size is greater than or equal to (4 decimal places)

Solution

The normal distribution can be approximated when np>=10 and n(1-p) >=10

here p=0.86 and 1-p = 1-0.86 = 0.14

sample size satisify the condition np>=10 ---> n>=10/0.86 =11.6279

sample size satisify the condition n(1-p)>=10 ---> n>=10/0.14 =71.8246

since it should satisfy the both conditions, the sample size is greater than or equal to 71.8246