Blood pressure is distributed normally, with a mean of 85 mm and a standard deviation of 20 mm. As a research physician, you are randomly assigned 100 patients. What is the probability that the average blood pressure for your sample of 100 patients is less than 82 mm?
2. Assume that the average weight of an NFL player is 245.7 lbs with a standard deviation of 34.5 lbs. The distribution of NFL weights is not normal. Suppose you took a random sample of 32 players. What is the probability that the sample average will be greater than 250 lbs? Round your answer to three decimal places, e.g. 0.192.
3. Suppose that X ~ N(5000, 400). You're considering taking a simple random sample and calculating the average of your sample. The Central Limit Theorem tells us that the distribution of all possible sample averages is normally distributed with a mean of 5000 and a standard deviation of 400/sqrt(100) = 400/10 = 40. What is the probability that you draw a sample with an average less than 4986?
4. A sample of 8 female college students consumes an average of 10 liters of alcohol per month, with a sample standard deviation of 3.9 liters. Monthly alcohol consumption is normally distributed. What is the margin of error for a 90% Confidence Interval for the mean? (Leave your answer to two decimal places, e.g. 18.12)
5. A weekly tabloid reported that the average income of its subscribers is $39,100. Assume this estimate of the mean household income is based on a sample of 70 subscribers, and, based on past studies, the population standard deviation is known to be sigma = $9,000. Construct a 95% confidence interval for the population mean.
$38,848 - $39,352
$36,949 - $41,251
$21,460 - $56,740
$36,992 - $41,208
6. A simple random sample of 20 romance novels has an average length of 250 pages long. Assume that the page count for all romance novels is normally distributed, with a standard deviation of 90 pages. Calculate a 90% confidence interval for the mean.
210 to 290
217 to 283
243 to 257
102 to 398