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Question: A city department of transportation research traffic congestion on a certain highway

Here is our question

A city department of transportation studied traffic congestion on a certain highway: To encourage carpooling, the department will recommend a carpool lane if the average number of people in passenger cars on the highway is less than 2. The probability distribution of the number of people in passenger cars on the highway is shown in the table

Let X = “The number of people in passenger cars in the highway”. Let Y the transformation of X by the rule Y = 75X + 5. Based on the new probability distribution, what is the men number of people in passengers cars on the highway?

• (A)7.04
• (B) 6 56
• (C) 4.7
• (D) 12.10
• (E) 6.28

Answer

a, You can use the formula for the above exercise:

with n=6, p= 0,6, q=0,2 we have

b, from the question, we have the table

and here is answer

c, we have number of reservation and probability like the table below. Firtly, we will find P when x=0 and x=1 like below:

and continue with x=2, x=3, x=4 and here is answer

Relevant knowledge

The probability of event A is a measure of the probability of event A occurring. In order to apply the classical definition of probability, the following two conditions must be met:

• The number of possible outcomes of the test is finite;
• The possible results of the test are equally likely.

Suppose A is an event involving a trial T and a trial T has a finite number of possible outcomes, which are equally likely. Then we call the ratio n(A)/n(Ω) is the probability of the event A
is denoted as P(A) =n(A)/n(Ω)
Where, n(A) is the number of elements of the set A, which is also the number of possible outcomes of the T-test favorable to the event A; and n(Ω) is the number of elements of the sample space Ω, which is also the number of possible outcomes of the T-test.

Conclusion

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