Answer to Question #136104 in Statistics and Probability for ervey

Question

You order some accessories online and get an estimated delivery date of June 1–June 11. You know you will be out of town June 4th, 5th, and 6th and are a little concerned about the package arriving when you are away. Assuming the delivery date follows a discrete uniform distribution, what is the likelihood your package will be delivered while you are out of town? Round your answer to four decimal places, if necessary.

Answer 1

Solution

X~ discrete uniform (1,11)

$$f(x) = {1 \over b-a+1}$$ $$f(x) = {1 \over 11-1+1}={1 \over 11}$$

The probability of the package arriving on any of the days is 1/11.

The number of days you'll be out of town is 3

Thus we calculate P(X=3)

$$F(x) =P(X \le x) ={ x-a+1 \over b-a+1}$$

$$={ x-1+1 \over 11-1+1}={x\over 11}$$

$$P(X \le 3)={3 \over 11} = 0.2727$$

Answer : 3/11 or 0.2727