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 $0.25 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. (Round your answers up to the nearest whole number.) (a) The desired margin of error is $0.10. (b) The desired margin of error is $0.06. (c) The desired margin of error is $0.05.

a) 25

b) 67

c) 97

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 $0.10.

This is n when M = 0.1. So

Rounding up to the nearest whole number, 25.

(b) The desired margin of error is $0.06.

This is n when M = 0.06. So

Rounding up, 67

(c) The desired margin of error is $0.05.

This is n when M = 0.05. So

Rounding up, 97