Question

Michelin Tire Company wishes to set a minimum mileage guarantee on its new MX100 tire. Tests reveal the mean mileage is 67,900 with a standard deviation of 2,050 miles and that the distribution of miles follows the normal probability distribution. Michelin wants to set the minimum guaranteed mileage so that no more than 4 percent of the tires will have to be replaced. What minimum guaranteed mileage should Michelin announce

Answer 1

Answer:

The minimum guaranteed mileage is  $x = 71489.55$

Step-by-step explanation:

From the question we are told that

   The mean is  $\mu = 67900$

     The standard deviation is  $\sigma = 2050$

Generally for the probability to be 4% the minimum guaranteed mileage is evaluated as

    $P( X \ge x ) =1- P( \frac{X - \mu }{\sigma } < \frac{ x - 67900 }{ 2050} ) = 0.04$

$\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )$

     $P( X \ge x ) =1- P( Z$

=>  $P( X \ge x ) = P( Z$

=>    $z = \frac{ x - 67900 }{ 2050}$

From the z table, the critical value corresponding to 0.96 to the left of the curve is  

         $z = 1.751$

So

        $1.751 = \frac{ x - 67900 }{ 2050}$

=>     $x = 71489.55$