Answer: 37
Step-by-step explanation:
As per given description in the question, we have
Population standard deviation : [tex]\sigma=2.6\text{ miles per gallon}[/tex]
Critical value for 98% confidence interval = [tex]z_{\alpha/2}=2.33[/tex]
Margin of error : E= 1 mile per gallon
Formula we use to find the sample size :
[tex]n=(\dfrac{z_{\alpha/2}\cdot \sigma}{E})^2[/tex]
i.e. [tex]n=(\dfrac{(2.33)\cdot(2.6)}{1})^2[/tex]
[tex]\Rightarrow\ n=36.699364\approx37[/tex]
Therefore , the number of automobiles should be used in the test =37
