1 A waiter estimates that about 95% of the guests at a large event will eat between 100 and 140grs. of meat. Based on the empirical rule what's your guesstimate for the standard deviation?

2 Assume that X is distributed normally with a mean of 50 and a standard deviation of 5. What is the probability that X <= 45? 45 <= X <= 55? X > 55? Lastly, suppose someone offers you money based on the realization of X. If X <= 45, you will receive $5 If 45 <= X <= 55, you will receive $8 If X > 55, you'll get $13 What's the expected amount of money you'll get?

3 A random sample of 247 adults was asked whether they would continue to travel abroad if the prices of flights increased 10%. 115 adults answered "yes". What is the probability that in reality less than 40% of adults in the population are willing to continue to travel abroad if the prices of flights increase by 10%?

4 Researchers know that the prevalence of COVID in population A is 5%, and that the prevalence of COVID in population B is 2%. A researcher flips a fair coin, if it lands on heads then he selects one person at random from population A and tests for COVID. If the coin lands on tails he follows the same protocol using a randomly selected person from population B. If the COVID test came back positive (and assuming that the test is 100% accurate), what is the probability that the coin landed in tails?