John Johnson, warden of Ramsey Prison, believes that a relationship exists between the size of the state’s population between the ages of 18 and 35 and the number of inmates assigned to Ramsey. John has his trusty analyst, Marc Wallace, go down to the Census Bureau’s local office to get census estimates for the past 50 years. Marc then regresses Ramsey’s prison population on the size of the state’s 18- to 35-year-old population. He finds the following:
 = -14 + .0005X
sb = .0000003 Sy|x = 12.6 r2 = .93
(a) The Census Bureau estimates that next year’s population between the ages of 18 and 35 will be 934,000. What is the projected prison population?
(b) Ramsey’s capacity is 500 persons. The old wing of the prison contains room for 100 persons. John would like to close this wing to save on maintenance. How small would the state’s 18- to 35-year-old population need to be for this to be done?