Question

An automobile manufacturer introduces a new model that
averages 27 miles per gallon in the city. A person who plans to
purchase one of these new cars wrote the manufacturer for the
details of the tests, and found out that the standard deviation is
3 miles per gallon. Assume that in-city mileage is approximately
normally distributed (use z score table)

a) What percentage of the time is the car averaging less than
20 miles per gallon for in-city driving.

b) What percentage of the time is the car averaging between 25
and 29 miles per gallon for in- city driving?

Answer #1

**Solution:-**

**Mean = 27, S.D = 3**

**a) The percentage of the time is the car averaging less
than 20 miles per gallon for in-city driving is 0.98%.**

**x = 20**

By applying normal distribution:-

z = - 2.333

**P(z < - 2.33) = 0.0098**

**P(z < - 2.33) = 0.98 %**

**b) The percentage of the time is the car averaging
between 25 and 29 miles per gallon for in- city driving is
49.52%.**

x_{1} = 25

x_{2} = 29

By applying normal distribution:-

z_{1} = - 0.667

z_{2} = 0.667

P( - 0.667 < z < 0.667) = P(z > - 0.667) - P(z > 0.667)

P( - 0.667 < z < 0.667) = 0.7476 - 0.2524

P( - 0.667 < z < 0.667) = 0.4952

P( - 0.667 < z < 0.667) = 49.52 %

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