Do this in jupyter notebook if possible or using python programming.

1) An airline runs a small commuter flight that has 10 seats. The probability that a passenger turns up for the flight is 0.92. What is the smallest number of seats the airline should sell to ensure that the probability the flight will be full is greater than 0.93?

2) The typical computer random number generator yields numbers in a uniform distribution between 0 and 1. If 45 random numbers are generated, find approximately the probability that their mean is below 0.465, using the central limit theorem.

3) A farmer is interested in knowing the mean weight of his chickens when they leave the farm. Suppose that the standard deviation of the chicken's weight is 500 grams. (a) What is the minimum number of chickens needed to ensure that the standard deviation of the sample mean is no more than 90 grams? (b) Suppose the farm has three coops. The mean weights in each coop are 1.75, 1.85 and 2.1 kg, and standard deviations are 450, 520, and 380 grams, respectively. Calculate the probability that a random sample of 30 chickens from the first coop will have a mean weight larger than 1.925 kg. Calculate the same probability for the second and third coops. (c) Suppose the proportion of the three coops are 0.60, 0.25, 0.15. Given that a random sample of 30 chickens from some coop has a mean weight larger than 1.925 kg, find the posterior probability the sample is from the (i) first coop, (ii) second coop, (iii) third coop. Which coop did the sample of chickens most likely have come from?

4) An engineering team has designed a lamp with two light bulbs. Let X be the lifetime for bulb 1 and Y be the lifetime for bulb 2, both in thousands of hours. Suppose that Xand Yare independent and they follow an exponential distribution with mean = 2. (a) What is the probability a bulb lasts more than 2000 hours? (b) If the lamp works when at least one bulb is lit, what is the probability that the lamp works for more than 2000 hours? (c) What is the probability that the lamp works no more than 1000 hours?