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%

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 %

Answer Link

IlaMends IlaMends · Answer 2 · 2019-01-25T08:06:54+01:00

Answer: The correct answer is option(a).

Explanation:

[tex]z_i=\frac{x_i-\mu}{\sigma }[/tex]

[tex]\sigma [/tex] = Standrad deviation

[tex]\mu[/tex] = Mean of the observations

[tex]x_1=38.7 mile/gallon[/tex]

[tex]z_1=\frac{38.7-43.8}{5.1}=-1[/tex]

[tex]x_2=48.9 mile/gallon[/tex]

[tex]z_2=\frac{48.9-43.8}{5.1}=1[/tex]

Using standard Z-table: for [tex]z_1[/tex] and [tex]z_2[/tex]

For [tex]z_1=-1[/tex] , the value from Z table = 0.1587

For [tex]z_2=1[/tex] , 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).