Homework 6

Suppose you give a survey to 700 randomly selected people on whether or not people drink soda. You know that 58% of the population drinks soda. Let X be the normal RV approximating the proportion of people in the survey who drink soda. What are the mean and variance of X?

In #1, what is the approx. probability that the proportion of people in this survey who drink soda is between 0.55 and 0.65? Supply your answer in terms of the Phi function.

Suppose 120 students take BIO 1111 where the historical failure rate is 31%. If each students performance is independent of each other, let X be the normal RV approximating the total number of students who fail. What are the mean and variance of X?

In #3 what is the approx. probability that the number of students who fail is less than or equal to 32? Supply your answer in terms of the Phi function and use the integer correction.

Suppose you run medical trials where 1170 people are tested for a reaction to a certain drug. If 219 people had a reaction, what is the sample proportion and sample variance (of the proportion, not the # of people) for this experiment?

In #5, what is the 95% confidence interval for the proportion of people who had a reaction?