In order to qualify for federal job training funds, a neighborhood group must provide an estimate of the mean of education level of unemployed youths less than or equal to 21 years old. The group plans to survey youth in its service area. The population of unemployed youth in the service area is estimated at 2,000. Previous studies have found that the standard deviation of years of education for this population is 10 years. If the neighborhood group must be 99% certain that their estimate is within one year of the actual mean, for approximately how many youths must the group obtain responses.

Question

In order to qualify for federal job training funds, a neighborhood group must provide an estimate of the mean of education level of unemployed youths less than or equal to 21 years old.  The group plans to survey youth in its service area.  The population of unemployed youth in the service area is estimated at 2,000.  Previous studies have found that the standard deviation of years of education for this population is 10 years.  If the neighborhood group must be 99% certain that their estimate is within one year of the actual mean, for approximately how many youths must the group obtain responses.