Given:
Standard deviation
[tex]\sigma=5.18[/tex]
Mean
[tex]\mu=129[/tex]
Required:
Find the longest braking distance one of these cars could have and still in the bottom.
Explanation:
The z-score formula is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Substitute the given values and find the value of z.
[tex]z=\frac{x-129}{5.18}[/tex]
This is the first percentile which is X when Z has a p-value of 0.01, so z = -2.327.
[tex]\begin{gathered} -2.327=\frac{x-129}{5.18} \\ x-129=-2.327(5.18) \\ x-129=-12.054 \\ x=129+12.054 \\ x=116.946\text{ ft} \end{gathered}[/tex]
Final answer:
The longest braking distance one of these cars could have and still in the bottom 1% is 116.946 ft.
