Automobile manufacturers have to design the driver’s seat area so that both tall and short adults can sit comfortably, reach all the controls and pedals, and see through the windshield. suppose a new car is designed so that these conditions are met for people from 58 inches to 76 inches tall. the heights of adult men in the united states are approximately normally distributed with a mean of 70 inches and a standard deviation of 3 inches. you can conclude that this design will work for about what % of men?

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?