As shown in the Venn diagram, 50% of the population is male, and 30% of the population is obese, 20% of males are obese.

1. What is the proportion of the population that are non-obese females. (2 points)
2. If I randomly select an individual from the population, and I know the person is obese, what is the probability that the person is female? (3 points)

Suppose UNC students’ heights are normally distributed, with a mean height of 70in (5’10”) and a standard deviation of 4in.
1. Calculate the Z score that can be used to assess the proportion of UNC students shorter than 68 in. (2 points)
2. Calculate the Z score that can be used to assess the probability of obtaining a random sample of 100 UNC students with average height less than 68 in. (2 points)
3. The standard normal distribution table is needed to tell exactly the proportion of UNC students shorter than 68in and the probability of obtaining a random sample of 100 UNC students with average height less than 68in. Without using such a table, can you tell which one is larger or whether they are the same? Explain why. (2 points)
4. I draw a random sample of 121 UNC freshmen. The sample’s average height is 71in, and standard deviation is 4in. Construct a 95% confidence interval and explain what the confidence interval tell you about the average height of UNC freshmen. (4 points)
5. I draw a random sample of 121 UNC freshmen. The sample’s average height is 71in, and standard deviation is 4in. Use a hypothesis test to examine whether the average height for freshmen is different from the average height of all UNC students? Make sure you clearly state your null and alternative hypotheses. (5 points)

To monitor a close election between two candidates, a news organization decides to take an opinion poll using a random sample of potential voters. The news organization wants the estimate be very precise—within ±1 percentage point (i.e. ±.01) with a 95% confident interval. What is the necessary sample size for this? Note: a close election assumes that either candidate has a 50 percent (i.e. p=.5) chance of winning.