Question

7. Avoiding an acci dent when driving can depend on reacti on time. That time, measured from the moment the driver first sees the danger until they get their foot on the brake pedal, is thought to follow a Normal distribution with a mean of 1.5 seconds and a standard deviation of 0.18 seconds. i (3 points) What percent of drivers have a reaction time less than 1.25 seconds? Report a percentage rounded to two decimal places ii. (3 points) What percent of drivers have reaction times between 1.6 and 1.8 seconds? Report a percentage rounded to two decimal places. i (3 points) What reaction time is at the 90 percentile? Report a time to the nearest hundredth of a second

Answer 1

Ans:

i)

z=(1.25-1.5)/0.18

z=-1.389

P(z<-1.389)=0.0824 or 8.24%

ii)

z(1.6)=(1.6-1.5)/0.18=0.556

z(1.8)=(1.8-1.5)/0.18=1.667

P(0.556<z<1.667)=P(z<1.667)-P(z<0.556)

=0.9522-0.7107=0.2415 or 24.15%

iii)

P(Z<=z)=0.9

z=normsinv(0.9)

P₉₀=1.5+1.282*0.18=1.73 seconds