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?
Answer by ikleyn(52878)   (Show Source):
You can put this solution on YOUR website! 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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(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. ANSWER
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. ANSWER
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. ANSWER
(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. ANSWER
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.
Solved, with complete explanations.
===================
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/
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