Q:

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.

Accepted Solution

A:
Answer: 0.2420Step-by-step explanation:Let x be a random variable that represents the number of cars passed through the intersection per day .As per given , we have[tex]\mu=550000[/tex][tex]\sigma=100,000[/tex]We assume that the number of cars on the interchange is approximately normally distributed.∡ [tex]z=\dfrac{x-\mu}{\sigma}[/tex]Then for x=  620,000, [tex]z=\dfrac{620000-550000}{100000}=0.7[/tex]  The probability more than 620,000 use the interchange on a random day :-[tex]P(x>620000)=P(z>0.7)=1-P(z\leq0.7)\\\\=1-0.7580363=0.2419637\approx0.2420[/tex]Hence, the probability more than 620,000 use the interchange on a random day= 0.2420