Question

1. A recent survey in Michigan revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. Find the following probabilities:

1. P(X = 10)
2. P(4 < X < 9)
3. P(X = 2)
4. P(3 ≤ X ≤ 6)

Answer 1

A recent survey in Michigan revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per That is n = 10 and p = 0.6 Let X be the number of vehicles that were exceeding the limit. Here X follows binomial distribution with parameters n = 10 and p = 0.6 P(x = 10) = (10)(0.6)0 (0.4) = 0.006047 b)We have to find the probability that P(4< X <9) P(4< X <9) = P(X = 5)+ P( X = 6) + P( X =7)+P ( X = 8) -3 (19)(0.0)*(0.4 jyou 2 = 0.2006 +0.2508 +0.215+0.1209 = 0.7874

c)

110 p(X = 10) = 100.600.40

p(X = 10) = 0.006

d)

p(3 < X < 6) = 10.6 0.410-1

p(3 < X < 6) = 0.0425 + 0.1115 +0.2007 +0.2508

p(3 < X < 6) = 0.6055