Based on the Normal model for car speeds (in km/h) on a road N(77,9.1) ,what are the cutoff values for the middle 70% of the speeds?

A) about 60.2 km/h,about 93.7 km/h
B) about 70.2 km/h,about 83.1 km/h
C) about 67.5 km/h,about 86.5 km/h
D) about 23.1 km/h,about 130.9 km/h
E) about 50.1 km/h,about 103.9 km/h

To find the cutoff values for the middle 70% of the speeds, we need to find the z-scores that correspond to the 15th and 85th percentiles of the standard normal distribution. We can use the formula z = (x - μ) / σ to standardize the values:
For the 15th percentile: z = invNorm(0.15) ≈ -1.04
For the 85th percentile: z = invNorm(0.85) ≈ 1.04

Substituting the given values, we get:
-1.04 = (x - 77) / 9.1, which gives x ≈ 67.5 km/h
1.04 = (x - 77) / 9.1, which gives x ≈ 86.5 km/h

Therefore, the cutoff values for the middle 70% of the speeds are about 67.5 km/h and about 86.5 km/h, which is option C.