Question

You run a shipping company that transports goods from China to the United States. The time it takes a shipment to reach the United States form China (in days) is normally distributed. The population of delivery times for all shipments has a mean of 40 days and a standard deviation of 6 days. If you sampled 100 random shipments, what is the probability that more than 58 of them take 40 days or more to reach their destination?

Answer 1

The probability that 40 days or more to reach their destination is

P(X > 40) = P(Z > (40-Mean) /SD)) = P(Z> (40-40)/6) = P(Z > 0) = 0.5

Now We sampled 100 random shipments i.e. n = 100, p = 0.5

Using Binomial to Normal approximation

The probability that more than 58 of them take 40 days or more to reach their destination is 0.04457