Gasoline Prices. The U. S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $2.94. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is $.25 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at 95% confidence. a.The desired margin of error is $.10.b. The desired margin of error is $.07.c. The desired margin of error is $.05.

a) Sample size of 96 or higher

b) Sample size of 196 or higher

c) Sample size of 385 or higher

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

In this problem,

a.The desired margin of error is $.10.

Sample size of n or higher when . So

b.The desired margin of error is $.07.

Sample size of n or higher when . So

c.The desired margin of error is $.05.

Sample size of n or higher when . So

Rounding up, sample size of 385 or higher

step-by-step explanation: