population sampling question

Homework sample size question

Hello I am having a difficulty with a homework problem from my basic statistics class. The problem: A weight loss trial involving a new diet is looking subjects. Population Mean weight is #240, Standard deviation 40, how many people need to be screened to meet criteria for body weight only? Criteria for inclusion in the study is weight greater than #300 and 200 people total are needed for the study.
300 is 1.5 Standard deviations from the mean so do I divide the standard deviation by 1.5 then square the number to get the number of people sampled? ie. (40/1.50) squared. =711 people

Any help you could lend would be most appreciated. Thank you in advance.

Last edited:


TS Contributor
You need to determine the % of the population that will be >= 300 lbs, based on the mean of 240 and sd of 40. Use the normal distribution table to figure this out.

Then, once you have this %, just figure out the screened sample size you would need in order to get 200 people who weigh at least 300 lbs.

Don't worry about margin of error here - it doesn't apply.
Thanks for the quick reply. This thing is driving me nuts and my professor is not good sticking to what is in our book (leaving me no good reference to consult). So I calculated a z score of 1.5 and went to my table under the normal curve and found a z of 1.5 gives me 0.9332 as a left tail probability. 1-0.9332 is equal to 0.0668 or 6.68%. I then found that 200 people is equal to 6.68% of 2994 people. So my final answer is 2994 as the number of people that need to be sampled? Is this all he wanted? Thanks again for all your help it is more than appreciated.