Question 3 According to the historical data, 72.9% of the 20-year-olds live until 65 years old. A random sample of size 70 was obtained. Let be the proportion of the sample that live until 65 years old. ) to describe the probability distribution of pand 1. Use the Central Limit Theorem (Select an answer Select an answer np>10 and n(1-p)>10 n(1-p)<10 but np>10 np<10 and n(1-p)<10 n(1-p)<10 but np>10 state its parameters and o: (Round the answers to 4 decimal places) p ~Select an answer Select an answer N X² unknown F T B (Hp σp 2. Find the probability that more than 85% of the sample live until 65 years old. (Round the answer to 4 decimal places)

It is known that the variable X is normally distributed as X-N (117, 8.4). If a sample size of 37 is selected then find the probability below P(X < 119)

Suppose that the lifetime of a component (in hours) is modeled with a Weibull distribution 4000. Determine the following in parts (a) and (b): with B 2 and 8 = = a P(X > 5000) b P(X> 8000|X > 3000) c Comment on the probabilities in the previous parts compared to the results for an expo- nential distribution.

Let X denote the waiting time (in minutes) for a customer. An assistant manager claims that μ, the average waiting time of the entire population of customers, is 2 minutes with standard deviation also 2 minutes. The manager doesn't believe his assistant's claim, so he observes a random sample of 36 custoers. The average waiting time for the 36 customers is 3.2 minutes. What is the probability that the average of 36 customers is 3.2 minutes or more? Do you think that assistant manager's claim that the mean is 2 minutes is correct?