Question 1206685: Avoiding an accident when driving can depend on reaction time. That time, measured from the moment the driver first sees the danger until he or she steps on the brake pedal, is thought to follow a Normal model with a mean of 1.5 seconds and a standard deviation of 0.18 second.
a, What percent of drivers have a reaction time less than 1.25 seconds?
b, What percent of drivers have reaction times between 1.6 and 1.8 seconds?
c, Describe the reaction times of the slowest 1/3 of all drivers.
Answer by ikleyn(52835)   (Show Source):
You can put this solution on YOUR website! .
Avoiding an accident when driving can depend on reaction time. That time, measured from the moment
the driver first sees the danger until he or she steps on the brake pedal,
is thought to follow a Normal model with a mean of 1.5 seconds and a standard deviation of 0.18 second.
(a) What percent of drivers have a reaction time less than 1.25 seconds?
(b) What percent of drivers have reaction times between 1.6 and 1.8 seconds?
(c) Describe the reaction times of the slowest 1/3 of all drivers.
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(a) This percent of drivers is the area under the described normal curve on the left of
z-score z < 1.25.
Use a regular calculator TI-83/84 and its standard function normcdf (Cumulative Distribution Function).
z1 z2 mean SD <<<---=== formatting pattern
The percent is the same as the probability P = normcdf(-9999, 1.25, 1.5, 0.18).
You will get P = 0.0824. ANSWER
Alternatively, you may use online free of charge calculator
https://onlinestatbook.com/2/calculators/normal_dist.html
which has simple interface and very informative visual output.
The answer produced by this online calculator is the same.
(b) This percent of drivers is the area under the described normal curve between
z-scores z 1.6 =< z <= 1.8.
Use a regular calculator TI-83/84 and its standard function normcdf.
z1 z2 mean SD <<<---=== formatting pattern
The percent is the same as the probability P = normcdf(1.6, 1.8, 1.5, 0.18).
You will get P = 0.2415. ANSWER
Alternatively, you may use online free of charge calculator
https://onlinestatbook.com/2/calculators/normal_dist.html
The answer produced by this online calculator is the same.
(c) In this part, they want you find a z-score under the described normal curve such that
the area under the normal curve on the  of this z-score be 1/3.
Use a regular calculator TI-83/84 and its standard function invNorm (inverse of Cumulative Distribution Function).
area mean SD <<<---=== formatting pattern
The desired z-score is z = invNorm(0.6667, 1.5, 0.18).
Notice that function invNorm accepts the area on the left only,
so we input the complementary probability/area 0.6667 = 1-0.333.
You will get z = 1.5775 of a second. ANSWER
Alternatively, you may use online free of charge calculator
https://onlinestatbook.com/2/calculators/inverse_normal_dist.html
which has simple interface and very informative visual output.
The answer produced by this online calculator is the same.
Solved.
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