Stat 185 - Practice sheet for Quiz 2

We'll have an online quiz on Wednesday. This will run very much like the last online quiz. The quiz will open at 8:00 AM on Wednesday and you'll have 45 minutes to complete it sometime by 1:00 PM. I assume that class time will be a convenient time to do that. I'll be available via email during class time so you can alert me to technical difficulties.

  1. Suppose that $X$ is normally distributed with a mean of $\mu=78.75$ and a standard deviation of $\sigma=3.82$. Compute $$P(70 < X < 80).$$
  2. Suppose a random sample of 209 Quarter Pounders from McDonalds finds a an average weight of 0.21 ounces with a standard deviation of 0.035 ounces. Use this data to write down a 96% confidence interval for the average weight of Quarter Pounders.
  3. According to FiveThirtyEight, a recent poll of 1500 adults conducted by YouGov for The Economist found an approval rating of 54% for Joe Biden. Use this data to construct a 97% confidence interval for Biden's approval rating.
  4. I'd like to construct a poll to determine a confidence interval for Joe Biden's approval rating. If I'd like the margin of error to be $\pm4\%$, how large should my sample size be?