Question 1: Let's say that in an area there is a male-to-female ratio of 12:13. An epidemic is spreading in this area with a 0.6% chance of infection in males and 0.35% in females. 1. Calculate the incidence of people in this area? 2. If you meet a person in the area who doesn't have the disease, the possibility that this person has sex | Which province is higher?

Question 2: The number of customers visiting a restaurant in the chain of restaurants of KFC Vietnam in one hour is a random variable X with a Poisson distribution. Know that there are 5 customers on average every 10 minutes.
1. Find the probability that 40 customers come to the restaurant in one hour.
2. Calculate the expectation and standard deviation of X.

Question 3: The diameter of a device manufactured by company B is a random variable X with a normal distribution with c = 0.01, Take one sample Randomly n=10 devices found an average diameter of 1.5045cm.
a. With a 95% confidence interval, find a symmetric confidence interval for the mean diameter (1) of the device.
b. At least how many of these devices must be taken to estimate the symmetric confidence interval for A with an error of not more than 0.003 given the 95% confidence interval.
c. Company B claims that the average diameter of each device is 1.5 cm. Test the above statement with significance level a=0.01.

When booking personal travel by air, one is always interested in actually arriving at one’s final destination even if that arrival is a bit late. the key variables we can typically try to control are the number of flight connections we have to make in route, and the amount of layover time we allow in those airports whenever we must make a connection. the key variables we have less control over are whether any particular flight will arrive at its destination late and, if late, how many minutes late it will be. for this assignment, the following necessarily-simplified assumptions describe our system of interest: the number of connections in route is a random variable with a poisson distribution, with an expected value of 1. the number of minutes of layover time allowed for each connection is based on a random variable with a poisson distribution (expected value 2) such that the allowed layover time is 15*(x+1). the probability that any particular flight segment will arrive late is a binomial distribution, with the probability of being late of 50%. if a flight arrives late, the number of minutes it is late is based on a random variable with an exponential distribution (lamda = .45) such that the minutes late (always rounded up to 10-minute values) is 10*(x+1). what is the probability of arriving at one’s final destination without having missed a connection? use excel.