A radar unit is used to measure speeds of cars on a motorway

A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is traveling at 80 km/hr?

Solution

Did you mean \"at most 80 km/hr\"?

If so, then this is the solution:

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    80      
u = mean =    90      
          
s = standard deviation =    10      
          
Thus,          
          
z = (x - u) / s =    -1      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1   ) =    0.158655254 [ANSWER]

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If you meant \"at least 80 km/hr\", this is the solution:

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    80      
u = mean =    90      
          
s = standard deviation =    10      
          
Thus,          
          
z = (x - u) / s =    -1      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1   ) =    0.841344746 [ANSWER]

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If you really meant what you wrote, the answer is 0, because we need an interval to get an area under the normal curve.