A large number of observations made on the speed of vehicles

A large number of observations made on the speed of vehicles at milepost 314 on I-80 yielded an average speed of 68.8 mph with a standard deviation of 13.0 mph. Assuming a normal distribution, how many vehicles out of every 100 will be exceeding 75 mph? Exceeding 85 mph?

Solution

Sol:

mean=68.8 mph

stddev=13.0 mph

n=sample size=100

P(X>75)

convert to zscore

z=x-mean/standard deviation

P(X>75) =P(z>75-68.8/13)

=P(z>6.2/13)

=P(z>0.4769)

P ( Z>0.4769 )=1P ( Z<0.4769 )=10.6844=0.3156

Forevery 100=100*0.3156=31.56=32 vehicles exceeeds 75mph

32 vehicles exceeds 75 mph

Solutionb:

P(X>85)=P(Z>85-68.8/13)

=P(Z>16.2/13)

=P(z>1.2462)

thai is

P ( Z>1.246 )=1P ( Z<1.246 )=10.8944=0.1056

for evry 100

100*0.1056=10.56=11 vehicles

11 vehicles out of 100 exceeds 85mph