Question

A construction zone on Interstate 15 has a speed limit of 40 mph. The speeds of vehicles passing through this construction zone are normally distributed with a mean of 44 mph and a standard deviation of 3 mph.

Required:
a. Find the percentage of vehicles who pass through this construction zone who are exceeding the posted speed limit.
b. What percentage of vehicles travel through this construction zone with speeds between 50 mph and 55 mph?

Answer 1

a. The percentage of vehicles who pass through this construction zone who are exceeding the posted speed limit =90.82%

b. Percentage of vehicles travel through this construction zone with speeds between 50 mph and 55 mph= 2.28%

Explanation:

We have to find

a) P(X>40)= 1- P(x=40)

Using the z statistic

Here

x= 40 mph

u= 44mph

σ= 3 mph

z=(40-44)/3=-1.33

From the z-table -1.67 = 0.9082

a) P(X>40)=

Probability exceeding the speed limit = 0.9082 = 90.82%

b) P(50<X<55)

Now

z1 = (50-44)/3 = 2

z2 = (55-44)/3= 3.67

Area for z>3.59 is almost equal to 1

From the z- table we get

P(55 < X < 60) = P((50-44)/3 < z < (55-44)/3)

= P(2 < z < 3.67)

= P(z<3.67) - P(z<2)

= 1 - 0.9772

= 0.0228

or 2.28%