SOLUTION: A recent survey in Malaysia revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 110 km per hour, we exceeding the limit. Suppose you randomly

Algebra ->  Probability-and-statistics -> SOLUTION: A recent survey in Malaysia revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 110 km per hour, we exceeding the limit. Suppose you randomly      Log On


   

Question 435687: A recent survey in Malaysia revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 110 km per hour, we exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on KL – Seremban highway where the speed limit is 110 km per hour. Let X denotes the number of vehicles that were exceeding the limit and follows a binomial distribution. Find the following probabilities:

a. P (X =10)
b. P (4 < x <9)
c. P (X = 2)
d. P (3 ≤ X ≤ 6)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Note: The probability of x successes in n trials is: 

P = nCx* p%5Ex%2Aq%5E%28n-x%29 where p and q are the probabilities of success and failure respectively. 

In this case p = .6 and q = .4

nCx = n%21%2F%28x%21%28n-x%29%21%29

X denotes the number of the ten vehicles randomly choses that were exceeding the limit 

a. P (X =10)  = (.6)^10

b. P (4 < x <9) = 252(.6)^5(.4)^5 + 210(.6)^6(.4)^4 +120(.6)^7(.4)^3 + 45(.6)^8(.4)^2



c. P (X = 2) = 45(.6)^2(.4)^8

d. P (3 ≤ X ≤ 6) = 

 120(.6)^3(.4)^7 + 210(.6)^4(.4)^6 + 252(.6)^5(.4)^5 + 210(.6)^6(.4)^4