Answer:
27.83 mpg is the minimum miles per gallon that puts a car in the top 30% of gas mileage.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 27.1 mpg
Standard Deviation, σ = 1.4
We are given that the distribution of miles per gallon is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.3
[tex]P( X > x) = P( z > \displaystyle\frac{x - 27.1}{1.4})=0.3[/tex]
[tex]= 1 -P( z \leq \displaystyle\frac{x - 27.1}{1.4})=0.3 [/tex]
[tex]=P( z \leq \displaystyle\frac{x - 27.1}{1.4})=0.7 [/tex]
Calculation the value from standard normal z table, we have,
[tex]\displaystyle\frac{x - 27.1}{1.4} = 0.524\\\\x = 27.83[/tex]
Thus, 27.83 mpg is the minimum miles per gallon that puts a car in the top 30% of gas mileage.
