Can anyone help me with this question using MATLAB? I'm not sure which function to use.

Wright et al. (A-2) used the 1999-2000 National Health and Nutrition Examination Survey (NHANES) to estimate dietary intake of 10 key nutrients. One of these nutrients was calcium (mg). They found in all 60 years or older a mean daily calcium intake of 721 mg with a standard deviation of 454 mg. Using these values for the mean and standard deviation for the U.S. population, find the probability that a random sample of size 50 will have a mean:

1) Greater that 900 mg.

2) Between 650mg and 850 mg

3) If the sample size is 20, does it affect your assumption on the sampling distribution of the sample mean?

Answer 1

[James Tursa]

Assuming the data is normally distributed, you could use the normcdf() function. You have to know how to calculate the mean and sd of a linear combination of variables (I assume you covered this in class?).

[Omar Abedalrahman]

the mean and standard deviation is already given

[James Tursa]

The mean and standard deviation of one random variable is given. You need to ask yourself the question: What is the mean and standard deviation of the average of 50 such variables? Of 20 such variables? Once you know that, then you can start to figure out the answers to the questions. Again, assuming the original distribution is normal, look at this link to get you started:

https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables

Or maybe this is an exercise in the Central Limit Theorem? Not clear from your post. In any event, you will be headed toward using normcdf(). Central Limit Theorem link:

https://en.wikipedia.org/wiki/Central_limit_theorem

Answer 2

[Star Strider]

You need to calculate the probability of the normal distribution exceeding those limtis. (For a population above about 30. the t-distributon approaches the normal distribution.)