The average retail price of gasoline all types for the first

The average retail price of gasoline (all types) for the first half of 2009 was 236.5 cents. What would the standard deviation have to be in order for there to be a 15% probability that a gallon of gas costs less than $2.00?

Solution

As

sigma = (x-u)/z

and for a left tailed area of 0.15, the corresponding z score is

z = -1.036433389

Thus,

sigma = (200 - 236.5)/(-1.036433389)

= 35.21692796 cents or $0.3521692796 [ANSWER]