In a large population, 81% of the households have cable tv. A simple random sample of 144 households is to be contacted and the sample proportion computed. What is the probability that the sampling distribution of sample porportions is less than 77%

The probability that the sampling distribution of sample porportions is less than 77% is P(p<0.77)=0.1106.

Step-by-step explanation:

We know that the population proportion is π=0.81.

We want to know the probability that the sampling distribution of sample proportions, with sample size n=144, is less than 0.77.

The sampling distributions of sampling proportions has a mean and standard deviation calculated as:

Then, we calculated the z-score for p=0.77:

The probability that the sample proportion is less than 0.77 is:

y= -