The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a mean of 24.6 mpg and a standard deviation of 11.2 mpg. if 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 27

 Mean (μ)= 24.6 mpg, Standard deviation(S.D) = 11.2 mpg and Sample size (n) = 30 , Average greater than 27

z(27) = (27 -μ)/(S.D/sqrt n)
z(27) = 27- 24.6/(11.2/sqrt30)
z(27) = 1.17
P(x-bar >27) = P(z> 1.17) = normal cdf (1.17, 100) = 0.4152