Answer: The correct answer is option(a).
Explanation:
\(z_i=\frac{x_i-\mu}{\sigma }\)
\(\sigma\) = Standrad deviation
\(\mu\) = Mean of the observations
\(x_1=38.7 mile/gallon\)
\(z_1=\frac{38.7-43.8}{5.1}=-1\)
\(x_2=48.9 mile/gallon\)
\(z_2=\frac{48.9-43.8}{5.1}=1\)
Using standard Z-table: for \(z_1\) and \(z_2\)
For \(z_1=-1\) , the value from Z table = 0.1587
For \(z_2=1\) , the value from Z table = 0.8413
Percentage of the automobiles have an average miles per gallon between 38.7 miles per gallon and 48.9 miles per gallon:
=0.8413 - 0.1587 = 0.6826 = 68.26 %
Hence, the correct answer option(a).
