The probability that a truck will be going over the speed limit on I-80 between Cheyenne and Rock Springs is 75%. Suppose a random sample of 5 trucks is observed on this stretch of I-80.

a) What is the probability that exactly 2 trucks are going over the speed limits?

The probability that exactly 2 trucks are going over the speed limit is 56.3% (rounding to the next tenth)

Step-by-step explanation:

1. Let's check all the information provided to us to answer the question correctly:

Probability that a truck will be going over the speed limit on I-80 between Cheyenne and Rock Springs = 75%.

Number of trucks in the random sample = 5

2. What is the probability that exactly 2 trucks are going over the speed limit?

Let's recall that two events are independent if the result of the second event is not affected by the result of the 1st event. If a first truck goes over the speed limit and a second truck does the same are independent events, the probability of both events occurring is the product of the probabilities of the individual events.

P (T₁ and T₂) = P (T₁) * P (T₂)

P (T₁ and T₂) = 0.75 * 0.75 = 0.5625

The probability that exactly 2 trucks are going over the speed limit is 56.3% (rounding to the next tenth)