Question

A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of $9$ km/hr and a standard deviation of $10$ km/hr. What is the probability that a car picked at random is travelling at more than $100$ km/hr?

• A. $0.1698$
• B. $0.1548$
• C. $0.1587$
• D. $0.1236$

Answer 1

The correct option is C $0.1587$

Let $x$ be the random variable that represents the speed of cars.
$x$ has $\mu =90,\sigma =10$.

We have to find the probability that $x$ is higher than $100$ or $P(x>100)$
Given $x,z=\frac{x-\mu }{\sigma }$.
Thus for $x=100,z=\frac{100-90}{10}=1$
$\Rightarrow P(x>100)=P(z=1)$
$=$ [total area]$-$[area to the left of $z=1$]

$=1-0.8413$ (from normal distribution table)
$\therefore P(x>100)=0.1587$
Hence the probability that a car selected at a random has a speed greater than $100$ km/hr is equal to $0.1587$.