## Elementary Statistics: Picturing the World (6th Edition)

The shortest braking distance of a sedan that can be in the top 10% is $131.88$ feet
A braking distance in the top 10% is any score above the 90th percentile. Thus, we have to find the z score that corresponds to the cumulative area 0.90. Using the standard normal table or technology we find that a z score of 1.28 corresponds to an area of 0.90. To find the corresponding $x$ value: z = $\frac{x - \mu}{\sigma}$ $x$ = $\mu$ + $z\sigma$ $x$ = $127 + (3.81 \times 1.28)$ $x$ = $131.88$ feet