Suppose the weight of TRes dinosaurs normally distributed wi

Suppose the weight of T-Res dinosaurs normally distributed with a mcan of u=12,000 pounds and a standerd deviation of phi=500 pounds If you bach in time and find 4 random T-Rexs and co,pate the x of their weights, What the that X will be between 11,500 and 12,500?

Solution

mean = 12000 and s.d = 500...

sample size = 4...
X-bar = sample mean...
P [ 11500 < X-bar < 12500 ] = P [ ( 11500 - 12000) / ( 500 / SQRT(4) ) < Z <  ( 12500 - 12000) / ( 500 / SQRT(4) ) ]

= P [ -2 < Z < 2 ] = P [ Z < 2 ] - P [ Z < -2 ] = 0.9544997.....