Question

The price of mid-grade gasoline is best characterized as having a normal distribution with mean a mean of 275 cents per gallon and a standard deviation of 11. Find the probability that the mid-grade gasoline at a randomly selected gas station is priced higher than 287 cents per gallon.
Round to 4 decimal places

Answer 1

Let X be the price of mid-grade gasoline, then X ~ N( 275,11²) . We will use the result Z = where and . We have to find the probability that the mid-grade gasoline at a randomly selected gas station is priced higher than 287 cents per gallon, i.e we have to find the probability

P ( X > 287 ) = P (Z > (287-275)/11) = P ( Z > 1.0901) = 1- P (Z <1.0901 ) = 1- 0.8622 = 0.1378 ( P (Z<1.0901) =0.8622 using standard normal tables)

Hence the probability that the mid-grade gasoline at a randomly selected gas station is priced higher than 287 cents per gallon is 0.1378.