Based on the Normal model for car speeds (in km/h)on a road N(77,9.1),what is the cutoff value for the highest 15% of the speeds?
A)about 67.5 km/h
B)about 86.5 km/h
C)about 11.6 km/h
D)about 65.5 km/h
E)about 63.1 km/h

Question

Quizplus · Accepted Answer

We need to find the cutoff value such that only the highest 15% of the speeds are included.

Using a standard Normal distribution table or calculator, we can find the z-score that corresponds to the 85th percentile (since 100% - 85% = 15%).

Doing so gives us a z-score of approximately 1.04.

Now we can use this z-score along with the mean and standard deviation of the Normal model to find the corresponding speed value:

z = (x - μ) / σ 
1.04 = (x - 77) / 9.1

Solving for x gives us x ≈ 86.5 km/h, which is the cutoff value for the highest 15% of speeds.

Therefore, the best choice is B.

Based on the Normal Model for Car Speeds (In Km/h)on