Question 1203181
A speed trap on the highway set by the O.P.P. shows that the mean speed of cars is
103.4 km/h with a standard deviation of 9.8 km/h. The posted speed limit on the
highway is 100 km/h.
a. What percentage of drivers are driving under the speed limit?
b. Speeders caught traveling over 15 km/h over the speed limit are subject to
losing demerit points. What percentage of speeders will be subject to
losing demerit points?
c. What percentage of drivers travel between the speed of 105 km/h and 115
km/h?
d. The top 2% of all drivers speeding are subject to losing their license.
According to the data, what speed must a driver be traveling to lose his or
her license?
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<pre>
(a)  This probability is the area under the specified normal curve on the left of
     the raw z-score of 100 km/h.

     To determine this probability (= this area), you may use your regular calculator 
     TI-83 or TI-84, standard function normalcdf. 
     Alternatively, you may use free of charge online calculator
     https://onlinestatbook.com/2/calculators/normal_dist.html 


     With TI-83 or TI-84, you have

                         z1     z2  mean   SD     <<<===--- formatting pattern
          P = normalcdf(-9999, 100, 103.4, 9.8) = 0.6357.   <U>ANSWER</U>

     With online calculator, you have the same answer PLUS a complete visual explanations
     on what you do, what the calculator does for you and why it is correct.


(b)  This percentage is the area under the specified normal curve on the right of
     the raw z-score 100 + 15 = 115 km/h.


     To determine this probability (= this area), you may use your regular calculator 
     TI-83 or TI-84, standard function normalcdf. 
     Alternatively, you may use free of charge online calculator
     https://onlinestatbook.com/2/calculators/normal_dist.html 


     With TI-83 or TI-84, you have

                         z1     z2  mean   SD     <<<===--- formatting pattern
          P = normalcdf( 115, 9999, 103.4, 9.8) = 0.0629.   <U>ANSWER</U>

     With online calculator, you have the same answer PLUS a complete visual explanations
     on what you do, what the calculator does for you and why it is correct.



(c)                       z1   z2  mean   SD     <<<===--- formatting pattern
          P = normalcdf( 105, 115, 103.4, 9.8) = 0.242.   <U>ANSWER</U>



(d)  To answer this question, you need to determine a raw z-score such that the area 
     under the normal curve is 2% on the right of it, or 98% on the left of it.


     To determine this z-score, you may use your regular calculator 
     TI-83 or TI-84, standard function invNorm. 
     Alternatively, you may use free of charge online calculator
     https://onlinestatbook.com/2/calculators/inverse_normal_dist.html


     With TI-83 or TI-84, you have

                       area  mean   SD     <<<===--- formatting pattern
          P = invNorm( 0.98, 103.4, 9.8) = 123.527.   <U>ANSWER</U>

     It is the maximum allowed speed. All drivers overspeeding are to lose his or her license.

     With online calculator, you have the same answer PLUS a complete visual explanations
     on what you do, what the calculator does for you and why it is correct.
</pre>

Solved, with complete explanations.


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To learn more on standard functions normalcdf and invNorm, look into these Internet web-sources


https://www.tcc.fl.edu/media/divisions/learning-commons/resources-by-subject/math/statistics/Choosing-whether-to-use-normalcdf-or-invNorm.pdf


https://courses.lumenlearning.com/introstats1/chapter/using-the-normal-distribution/