Two-Lane Highway Speed.The Iowa Department of Transportation is considering changing the speedlimit on the two-lane highways in the state. They decide to take a random sample of cars on two-lane highways across the state and record the cars' speeds in miles per hour (mph). In a random sampleof 16 cars, the recorded speeds had a mean of 49.79 mph. The speed of all cars on two-lane highwaysin Iowa is known to be normally distributed with a standard deviation of 3.732 mph.

What should be the sample size used by DOT if they desire to obtain a 90% confidence interval for the mean speed with a width of at most 1.5 mph?

Keep 4 decimals in your intermediate calculations and report your final answer as an integer (whole number). Remember to always round UP to the closest integer (whole number) when computing minimum sample sizes.