The Nissan Leaf (Leading. Environmentally friendly. Affordable, Famlly car) Is a

Question

The Nissan Leaf (Leading. Environmentally friendly. Affordable, Famlly car) Is a five-door hatchback electric car manufactured by Nissan and Introduced in 2010. The comblned fuel economy of the Nissan Is 99 mlles per gallon (mpg) gasolne equlvalent. Assume the mpg for the NIssan Leaf Is normally distributed with mean 99 and standard deviation 8, N(99, 8). The cumulative distribution function, Fx) for a normally distributed random varlable with mean 99 and standard devlation 8 can be generated with the Excel function: NORMDIST.99,8,TRUE) and is given below. (NOTE: the random variable X is a continuous random varlable). a.Use the Excel function NORM.DIST to find P(X 95). (1 point) b.Use the Excel function NORM.DIST to find P(97 X 101). (1 point) c.Use the Excel function NORM.DIST to find PX 105). (1 point) d.Use the Excel function NORM.DIST to find P(X 105) If the mpg for the Nissan Leaf Is normally distributed with mean 99 and standard deviation 2.As a Nissan Leaf owner, would you be more confident that you would get 105 mpg or better if mpg was distributed N(99, 8) or N(99, 2)? Explairn how you reached your conclusion. (1 point) e-Find the mpg that the lower 5% of Nissan cars achieve if mpg is distributed N(99,8) (1 point) (Find the mpg that the upper 5% of Nissan cars achieve if mpg is distributed N(99,8), (1 point) g.Use the standard normal distribution to answer a-d (4 points)

Explanation / Answer

A. To calculate P(X<95) use excel function: =NORM.DIST(95,99,8,TRUE) which results to 0.308538

B. To find P(97 < X < 101) we can calculate P(X< 101) - P (X<97)

=NORM.DIST(101,99,8,TRUE) - NORM.DIST(97,99,8,TRUE)

=0.598706-0.401294

=0.197413

c. As we know P under the normal distribution is 1.

So to calculate P(X>105) = 1 - P(X<105)

= 1 - NORM.DIST(105,99,8,TRUE)

=1-0.773373 = 0.226627

d. if m=99 and sd = 2

P(X>105) = 1 - NORM.DIST(105,99,2,TRUE) = 0.00135

When the sd is less, most of the cars will fall within the first SD which will be closer to economy rate. If the sd is more the cars will have economy rate more from 99 - 8 to 99 + 8

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