I would appreciate if anyone could help me with the following questions please.

NASA is interested in the true proportion of children who are interested in becoming astronauts. At a 90% confidence level, what is the minimum sample size they need such that the population proportion is within 2.7% of the estimated proportion? O a. 928 O b. 928 O C. 927 O d. None of the other choices The weight of a pomelo is normally distributed. A consumer is interested in the average weight of pomelos. In a random sample of twelve pomelos, the average weight is determined to be 1301 g with a standard deviation of 168 g. Construct a 99% confidence interval for the population mean weight. O a. (1257.5160, 1344.4840) O b. (1150.3670, 1451.6330) O c. (1152.8404, 1449.1596) O d. (1176.0706, 1425.9294) A 95% confidence interval for p1 - pz is calculated to be (0.1823, 0.3001). If the level of confidence is now decreased to 90%, what happens to the confidence interval? O a. Unknown O b. It increases in size O c. It decreases in size O d. It remains the same For the variables X and Y, if the slope of the LS regression line is negative, what does this imply about the correlation? O a. None of the other choices O b. The correlation is positive O c. The correlation is zero O d. The correlation is negative