Suppose that 2224 of all vehicles on the road get fuel econo

Suppose that 22.24% of all vehicles on the road get fuel economy of atlas 35 miles per gallon. You conduct an observational study on a stretch of road outside of campus and record the make and model of 796 vehicles over a month long period. What is the probability that less than 21.34% of the cars you observed get at least 35 mpg?

Solution

Normal Distribution
Proportion ( P ) = 0.2224
Standard Deviation ( sd )= Sqrt (P*Q /n) = 0.2224*0.7776/796
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 0.2134) = (0.2134-0.2224)/0.0147
= -0.009/0.0147= -0.6122
= P ( Z <-0.6122) From Standard Normal Table
= 0.2702

the probability that less than 21.34% of the cars you observed get at least 35 mpg ~ 27.02%