Question

The average miles per gallon of a particular automobile model are approximately normally distributed with a given mean mc024-1.jpg = 43.8 miles per gallon and standard deviation mc024-2.jpg = 5.1 miles per gallon. What percentage of the automobiles have an average miles per gallon between 38.7 miles per gallon and 48.9 miles per gallon?

a.68%
b.75%
c.95%
d.100%

Answer 1

Answer: The correct answer is option(a).

Step-by-step explanation:

`z_i=(x_i-\mu)/(\sigma )`

`\sigma` = Standrad deviation

`\mu` = Mean of the observations

`x_1=38.7 mile/gallon`

`z_1=(38.7-43.8)/(5.1)=-1`

`x_2=48.9 mile/gallon`

`z_2=(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).

Answer 2

Mean = 43.8 miles per gallon
Standard Deviation = 5.1 miles per gallon
This is a normal distribution and those values ( 38.7 and 48.9 ) are less than one standard deviation away from the mean value:
M - 1 SD = 43.8 - 5.1 = 38.7
M + 1 SD = 43.8 + 5.1 = 48.9
34 % + 34 % = 68 %
Answer:
A ) 68 %