Answer: 37
Step-by-step explanation:
Given : Significance level : [tex]\alpha:1-0.98=0.02[/tex]
Critical value : [tex]z_{\alpha/2}=z_{0.01}=2.33[/tex]
margin of error : E= 1 mile per gallon
Population standard deviation: [tex]\sigma=2.6[/tex] miles per gallon.
We know that when the population standard deviation is known then the formula to find the sample size is given by :
[tex]n=(\dfrac{z_{\alpha/2}\times \sigma}{E})^2[/tex]
[tex]n=(\dfrac{(2.33)\times 2.6}{1})^2=36.699364\approx37[/tex] [Round to the next whole number.]
Hence, the required number of automobiles should be used in the test = 37
