Central limit theorem

[stats2050]

The amount of coffee that people drink per day is normally distributed with a mean of 16 ounces and a standard deviation of 4 ounces. 18 randomly selected people are surveyed. Round all answers to 4 decimal places where possible.

1. What is the distribution of XX? XX ~ N( , )
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
3. What is the probability that one randomly selected person drinks between 15 and 17 ounces of coffee per day?
4. For the 18 people, find the probability that the average coffee consumption is between 15 and 17 ounces of coffee per day.
5. For part d), is the assumption that the distribution is normal necessary? NO OR YES
6. Find the IQR for the average of 18 coffee drinkers.
   Q1 = ? ounces
   Q3 = ? ounces
   IQR: ? ounces

 

[tkhunny]

What are "XX" and "¯xx¯ "? I could guess, I suppose. Definitions are often helpful. Is any of this information simply given in the problem statement?

What's the difference between the standard deviation of a single, sampled individual and the standard deviation of the mean of a random sample of size 18?

"For part d)" - There isn't a "part d)". You entitled the question "Central Limit Theorem". Is there a clue in there?

Please write a better problem statement and please show YOUR work. We're not a homework service and we do not intend to be your primary instructors. Show us where you are. You cannot have nothing to offer.

Is an IQR typical of a continuous distribution?