1. The spacing distance between two consecutive vehicles on a road follows a log

Question

1. The spacing distance between two consecutive vehicles on a road follows a logarithmic normal distribution with the mean value 200ft and a standard deviation of 50ft. A connection between two consecutive vehicles is successfully created if the spacing distance between them is less than 230ft mile. Consider a fleet of vehicles including 5 vehicles. A connection of the fleet will be broken up if any two consecutive is not successfully connected. Calculate the probability of the event that the fleet is well connected from vehicle 1 to vehicle 5. The connection between any two consecutive vehicles is independent.

2. A survey of Costco dedicated that: The number of event that a person bought beer is third times as the event that he/she bought diaper. We assume that the event that a person bought beer is independent of the event that he/she bought diaper. We know the probability that a person bought both diaper and beer is 0.12 What is the probability that a person bought neither beer nor diaper?

3. There are three events: A, B, and C. The probability that event A occurs is 20% while probability that event B occurs is 25%. A and B are independent. If only event A or B occurs, the probability that event C occurs is 15%. If both A & B occurs, there is 60% chance that C would occur. C would not occur if neither A nor B occurs. What’s the probability that C does NOT occur?

4. The number of typographical errors in new editions of textbooks is Poisson distributed with a mean of 1.2 typos per 100 pages. The instructor randomly selects 600 pages of a new book. What is the probability that there are no typos?

5. Random Variable X follows Normal distribution with mean =3 and variance = 25, what is the probability of P(4 X9 )

6. The duration of an activity in a construction project is determined to have three possibilities with equal chances. These are 65, 74 and 85 days. The completion time for the project has two possibilities, 70 or 82 days with equal chances. The probability that the activity will be completed on time for the project is most nearly.

Explanation / Answer

5) mean = 3

standard deviation = 25

we need to find p(4<=x<=9)

as the distribution is normal the formula to be used

z = (x-mean)/standard deviation

For x = 4, z = (4 - 3) / 5 = 0.2 and for x = 9, z = (9 - 3) / 5 = 1.2

Hence P(4 <= x <=9) = P(0.2 < z < 1.2) = [area to the left of z = 1.2] - [area to the left of 0.2]

= 0.8849 - 0.5793 = 0.3056

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