The United States Postal Service reports 95% of first-class mail within the same city is delivered within two days of the time of mailing. Six letters are randomly sent to different locations. 1. What is the probability that all six arrive within two days? 2. What is the probability that exactly five arrive within two days? 3. Find the mean number of letters that will arrive within two days. 4. Compute the variance and standard deviation of the number that will arrive within two days.

Step-by-step explanation:

This is a binomial probability distribution because the outcome is either a randomly selected first-class mail within the same city is delivered within two days of the time of mailing or more days. The probability of success, p is that it is delivered within 2 days. Therefore,

p = 95/100 = 0.95

q(probability of success) = 1 - p = 1 - 0.95 = 0.05

n = number of samples = 6

1)The probability that all six arrive within two days, P(x = 6) would be determined from the binomial probability distribution calculator. Therefore,

P(x = 6) = 0.74

2) P(x = 5) = 0.23

3) mean = np = 6 × 0.95 = 5.7

4) Variance = npq = 6 × 0.95 × 0.05 = 0.285

Standard deviation = √0.285 = 0.53

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step-by-step explanation: