Probability and Statistics: Sampling and the Central Limit Theorem
What is the probability that a random selection of 32 women have an average age at first marriage between 26 and 27?
Given a uniform distribution ranging from 0 to 1, collect 20 random samples and calculate the mean of these samples. Repeat this to collect additional samples and calculate more means, then draw a histogram of these means. Discuss how the means are distributed after multiple iterations.
Using an exponential distribution, collect 20 random samples and calculate the mean of these samples. Repeat the process to collect more samples and calculate more means, then draw a histogram of these means. Analyze the distribution of these means after several iterations.
A statistics class has six students with the ages [18, 18, 19, 20, 20, 21]. Construct a sampling distribution of the mean of age for samples with the size of two.
You are planning a full day nature trip for 50 men. The average male drinks 2 liters of water when active outdoors with a standard deviation of 0.7 liters. You will bring 110 liters of water. What is the probability that you will run out of water?
What is the probability that our sample proportion of 0.54 is within two standard deviations of the population proportion?
Suppose it is known that the heights of all Canadians follows a normal distribution with a mean of 160 centimeters and a standard deviation of 7 centimeters. What is the probability that the average height of 10 random Canadians is less than 157 centimeters?
What is the probability that the mean of 9 randomly selected orders is at least 760 calories?
90% of all plant species are classified as angiosperms. If you randomly sample 200 plants from all known plant species, what is the probability that at least 95% will be flowering plants?
In a certain University, the mean age of students is 20.5 with a standard deviation of 0.8. Calculate the standard error of the mean if a sample of 25 students were selected.
What would the standard error of the mean be if a sample of 100 students were selected, given the population standard deviation is 0.8?
Suppose we want to learn about the proportion of people who like to dance in the population, which unbeknownst to us is 60%. If we take a sample of a few people, the proportion of them who like to dance will, on average, be 60%.