Question

A radar unit is used to measure the speed of cars at NLEX. NLEX records show that the measures of speed are normally distributed with a mean of 94 km/hr and a standard deviation of 12 km/hr. The speed of the top 15% drivers are considered over speeding and are apprehended. Therefore, for a driver of the car to be charged of over speeding, his speed should be a minimum of Blank 1 km/hr. Round off your answer to two (2) decimal places.

Answer 1

Let $X=$ the speed of car: $X\sim N(\mu, \sigma^2).$

Given $\mu=94, \sigma=12$

$$P(X>x)=1-P(X\leq x)$$

$$=1-P(Z\leq \dfrac{x-\mu}{\sigma})$$

$$=1-P(Z\leq \dfrac{x-94}{12})=0.15$$

$$P(Z\leq \dfrac{x-94}{12})=0.85$$

$$\dfrac{x-94}{12}\approx1.036433$$

$$x=94+12(1.036433)$$

$$x=106.44$$

His speed should be a minimum of $106.44$ km/hr.