After increased patrol,33% of vehicles on a road travel below 45 km/h with a standard deviation of 5.1 km/h.Assuming a Normal model is appropriate,find the mean speed.
A)1.68 km/h
B)47.24 km/h
C)-42.76 km/h
D)50.1 km/h
E)14..85 km/h

Question

Quizplus · Accepted Answer

We know that 33% of the vehicles travel below 45 km/h. This means that the remaining 67% of the vehicles travel at or above 45 km/h.

Let X be the speed of a vehicle. We are given that the standard deviation of X is 5.1 km/h.

Using a standard normal distribution table, we can find the z-score corresponding to the 67th percentile, which is approximately 0.44. This means that:

z = (X - μ) / σ = 0.44

where μ is the mean speed.

Rearranging this equation, we get:

μ = X - (0.44)σ

Substituting X = 45 and σ = 5.1 km/h, we get:

μ = 45 - (0.44)(5.1) = 42.76 km/h

Therefore, the mean speed is approximately 42.76 km/h. The closest answer choice is B: 47.24 km/h.

After Increased Patrol,33% of Vehicles on a Road Travel Below