Question

The East Los Angeles Interchange is the busiest freeway interchange in the world. In 2008, an average of 550,000 cars passed through the intersection per day with a standard deviation of 100,000. What is the probability more than 620,000 use the interchange on a random day? Assume the number of cars on the interchange is approximately normally distributed.

Answer 1

Answer: 0.2420

Explanation:

Let x be a random variable that represents the number of cars passed through the intersection per day .

As per given , we have

`\mu=550000`

`\sigma=100,000`

We assume that the number of cars on the interchange is approximately normally distributed.

∵
`z=(x-\mu)/(\sigma)`

Then for x= 620,000,
`z=(620000-550000)/(100000)=0.7`

The probability more than 620,000 use the interchange on a random day :-

`P(x>620000)=P(z>0.7)=1-P(z\leq0.7)\\\\=1-0.7580363=0.2419637\approx0.2420`

Hence, the probability more than 620,000 use the interchange on a random day= 0.2420