contestada

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.

Respuesta :

JeanaShupp

Answer: 0.2420

Step-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

Otras preguntas

Q&A Education