Question

The miles per gallon(mpg) measurement for the fuel economy for a brand of compact car is approximately normally distributed with the mean u= 26.7 mpg and standard deviation o=7.2 mpg Let x= fuel economy( in miles per gallon) A) what percent of compact cars( for this brand) have a fuel economy grater than 26.7 mpg?Answer: ( include the percent (%) symbol in your answer) B) What is the z-score( or standard score) for fuel economy of 25 mpg ( rounded to 2 decimal places)?Answer: z= C) find the probability that a random selected new compact ( from this brand) has a fuel economy less than 25 mpg. Write your answer as a complete probability statement. Do not round your answer. Answer:

Answer 1

Given

mean = 26.7 mpg

standard deviation =7.2 mpg

Find

a) what percent of compact cars( for this brand) have a fuel economy greater than 26.7 mpg

b) What is the z-score( or standard score) for fuel economy of 25 mpg

c) find the probability that a random selected new compact ( from this brand) has a fuel economy less than 25 mpg.

Step-by-step explanation

a)

mean = 26.7 mpg

standard deviation =7.2 mpg

P(X > 26.7) =

`\begin{gathered} P\left(X>26.7\right)=P((X-\mu)/(\sigma)>(26.7-26.7)/(7.2)) \\ \\ =P(Z>0) \\ =0.5 \end{gathered}`

b)

`\begin{gathered} z=(X-\mu)/(\sigma) \\ =(25-26.7)/(7.5) \\ =-0.22667 \\ =-0.23 \end{gathered}`

c)

`\begin{gathered} P(Z<-0.23)=P(Z>0.23) \\ =1-P(Z\leq0.23) \\ =1-0.590954 \\ =0.409046 \\ =0.40905 \end{gathered}`

Final Answer

a)

b)

c)0.40905