After increased patrol,cars on a road travel at speeds averaging 55 km/h.If 93% of vehicles travel below 68 km/h,what approximate standard deviation could represent this model (assuming a Normal model is appropriate)?
A)30.41
B)8.78
C)63.24
D)51.15
E)-8.78

Question

Quizplus · Accepted Answer

Since we are assuming a Normal model is appropriate, we can use the formula:
z = (x - μ) / σ
where x is the speed, μ is the mean speed (55 km/h) and σ is the standard deviation.
We know that 93% of vehicles travel below 68 km/h. To find the corresponding z-score, we use the standard normal distribution table or calculator:
z = (68 - 55) / σ
Using a standard normal distribution table or calculator, we find that the z-score is approximately 1.5.
From the same table, we find that the corresponding percentile for a z-score of 1.5 is approximately 93.3%, which is very close to the given percentage of 93%.
Therefore, we can estimate the standard deviation as:
1.5 = (68 - 55) / σ
σ ≈ 8.78
So the best choice is B, with an approximate standard deviation of 8.78.

After Increased Patrol,cars on a Road Travel at Speeds Averaging