A traffic study conducted at one point on an interstate highway shows that vehicle speeds (in mph) are normally distributed with μ = 66.7 and s =5.0. If a vehicle is randomly checked, what is the probability that its speed is between 42.0 and 69.0?

We can find the z-scores associated with each of the values 42 and 69. The z-score is given by:

z = (value - mean)/sd

= (42-66.7)/5 and (69-66.7)/5

= -4.94 and 0.46

Next find P(-4.94<z<0.46)

= P(z<0.46) - P(z<-4.94)

(calculate these directly or use a z-table; remembering that P(-z) = 1-P(z) )

= 0.677 - 0.000

= 0.677

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