Explain whether or not each of the following scenarios meets the conditions for which the sampling distribution of the sample proportion is approximately normal. If not, explain which condition is violated.
a. Unknown to the government, 10% of all cars in a certain city do not meet appropriate emissions standards. The government wants to estimate that percentage, so they take a random sample of 30 cars and compute the sample proportion that do not meet the standards.
b. The U.S. Census Bureau wants to estimate the proportion of households that have someone at home between 7:00 P.M. and 7:30 P.M. on weeknights to determine whether or not that would be an efficient time to collect census data. They survey a random sample of 2000 households and visit them during that time to see whether or not someone is at home.
c. You want to know what proportion of days in typical years have rain or snow in the area where you live. For the months of January and February, you record whether or not there is rain or snow each day, and then you calculate the proportion.
d. A large company wants to determine the proportion of its employees who are interested in on-site day care. For a random sample of 100 employees, the company calculates the sample proportion who are interested.