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Applying the Central Limit Theorem

Example:  According to the United States Department of Agriculture, the mean calorie intake of males 20-39 years old is

, with standard deviation .  Suppose a nutritionist conducts a simple random sample of   males between the ages of 20 and 39 years old and obtains a sample mean .  What is the probability that a random sample of 35 males between the ages of 20 and 39 years old would result in a sample mean of 2750 or higher?  Are the results of the survey unusual?  Why?

The calorie intake of 20-39 year old males is described as a population with a mean,  and a standard deviation,   A sample of 35 males is selected from the population and the calorie intake of each male is recorded.  What is the probability that the sample average,  ,  is 2750 calories or higher?

Since , you can conclude that the sampling distribution of the sample mean is approximately normal with  and    

To calculate , press 2^nd [DISTR], select 2:normalcdf( and type in

 and press ENTER.