Solved: Vehicle speed on a particular bridge in China can

Step 1 of 3

         Let X be the vehicle speed, which follows normal distribution. Here it is given that 5% of all vehicles travel less than 39.12m/h and 10% travel more than 73.24 m/h. We have to find the mean and standard deviation.

It is given that

 P(X<39.12) = 0.05

 P(X>73.24) =.1

Consider,

 P(X<39.12) = 0.05

 P(< ) = 0.05

         P( Z<  ) = 0.05

From the standard normal table we will get

P(Z< -1.645) = 0.05

So

     = -1.645

              = 39.12+1.645  …….  (1)

Similarly

      Consider

       P(X>73.24) = .01

        P(< ) = 0.1

                P( Z>  ) = 0.1

  From the standard normal table we will get

  P(Z> -1.28) = 0.1

So

    = -1.28

 =  73.24+1.28 ……… (2)

By solving equation  (1) and (2) we can find the values of  and .

39.12+1.645 = 73.24+1.28

34.12 = 0.36

      =  94.78

Apply this to any of the equation you will get the value of  = 194.55

 So

Mean = 194.55

Standard deviation = 94.78