Statistics- Sampling Distributions

Question

   Hi!

I am in a college statistics class and we have just finished covering sampling distributions. I am trying to work through my homework problems right now and am totally lost! I know the central limit theorem formula, but I don't know when to use it. Also, I am really super stuck on this one problem and don't know what to do. I think part of the issue might be that I don't understand what the problem is actually asking me to do. =)   Here is the problem:

 

 

Shelia’s measured glucose level one hour after having a sugary drink varies according to the Normal distribution with μ = 122 mg/dl and μ = 12 mg/dl. What is the level L such that there is probability only 0.05 that the mean glucose level of 4 test results falls above L? (Hint: This requires a backward Normal calculation.

   Thanks,

   Hannah =)

Answer 1

Hi Hannah,

           We are talking about the mean or average of 4 measurements taken from a population whose mean and standard deviation are known i.e. μ=122 and σ=12. These are called the population parameters and are symbolized using greek letters. This might be the result of 1000's of measurements taken over a long period of time. Now when you sample by taking 4 measurements from a population that has a mean of 122 and a standard deviation of 12 that the sample standard deviation, s will have a value of σ/√4 or σ/2. This is the central limit effect.

        Now back to the problem. I assume you have learned about the Z score. Z=(L-μ)/s and is a measure of how far your measurement is from the mean in multiples of standard deviations. So the question is asking for the value of L that makes the probability of Z, P(Z≥.05) You now have to look in a normal probability table to find the Z that corresponds to P(Z>.05) and that Z=1.645. So now you can solve for L=1.645*s+μ =1.645*2+122=125.29.

        Hope this helps

Jim