Let X be the miles per gallon of a particular vehicle Suppos

Let X be the miles per gallon of a particular vehicle. Suppose . Find if .

Solution

population mean,u = 18.5
standard deviation,sigma = 2.2
sample size,n = 5

standard error = sigma/sqrt(n) = 0.9839

P( 18.2 <X< 19 )
= P( ((18.2-18.5) / 0.9839) <Z< ((19-18.5) / 0.9839) )
= P( -0.30 <Z< 0.51 )
= P(Z<0.51) - P(Z<-0.3)
= P(Z<0.51) - (1 - P(Z<0.3))
= 0.695 - ( 1 - 0.6179)
= 0.695 - 0.3821
= 0.3129

To find P(Z<0.51) look in the standard normal table in the row 0.50 and column 0.01(0.51 = 0.50+0.01), the value obtained is 0.6950