Answer:
The Sample size is 1918.89035
Step-by-step explanation:
Consider the provided information.
It is given that 14 out of 105 samples failed.
Therefore p = 14/105 = 0.13 3... and q=1-0.133=0.867
Samples would be needed to create a 99 percent confidence interval.
Subtract the confidence level from 1, then divide by two.
By standard normal table z=2.5758≈2.58
Calculate the sample size as:
Where, e is the margin of error,
Substitute the respective values.
Hence, the Sample size is 1918.89035
Answer:
It takes less time sending 5 letters the traditional way with a probability of 36.7%.
Step-by-step explanation:
First we must take into account that:
- The traditional method is distributed X ~ Poisson(L = 1)
- The new method is distributed X ~ Poisson(L = 5)
Where L is the intensity in which the events happen in a time unit and x is the number of events.
To solve the problem we must calculate the probability of events (to send 5 letters) in a unit of time for both methods, so:
- For the traditional method:
- For the new method:
According to this calculations we have a higher probability of sending 5 letters with the traditional method in a unit of time, that is 36.7%. Whereas sending 5 letters with the new method is less probable in a unit of time. In other words, we have more events per unit of time with the traditional method.