Question

20 cars are tested for their mileage the mileage follows a normal distribution with an average of 12 km per hour and a standard deviation of 3 kilometre per hour

Answer 1

Step-by-step explanation:

Let x be the random variable that represents the speed of cars.

x has μ=90,σ=10.

We have to find the probability that x is higher than 100 or P(x>100)

Given x,z=

σ

x−μ

.

Thus for x=100,z=

10

100−90

=1

⇒P(x>100)=P(z=1)

= [total area]−[area to the left of z=1]

=1−0.8413 (from normal distribution table)

∴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.