Question

A radar unit is used to measure speeds of cars on a motorway. The

speeds are normally distributed with a mean of 90 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?​

Answer 1

Answer:

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=σx−μ.

Thus for x=100,z=10100−90=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.

Answer 2

Answer:

answer is in given photo above

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