# The United States Postal Service

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The United States Postal Service reports 95 percent of first class mail within the same city are delivered within two days of the time of mailing. Six letters are randomly sent to different locations.

a. What is the probability that all six arrive within two days?

b. What is the probability that exactly five arrive within two days?

c. Find the mean number of letters that will arrive within two days.

d. Compute the variance and standard deviation of the number that will arrive within two days.

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Can you please give a DETAILED explaination to how you arrived at the answer to this problem.

The United States Postal Service reports 95 percent of first class mail within the same city

is delivered within two ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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