Hi, any help regarding these 2 questions is much appreciated!
Q1. I own 36 gease who each lay one golden egg in a week. I knows that 1 in 6 of these eggs is a bad egg and must be discarded. Let X be the number of good eggs I get in a week.
a) State distribution of X
b)(i)How many good eggs can I expect to get in a week?
(ii)What is the variance of the number of good eggs I get in a week?
c)(i)What is the probability that I will get 36 good eggs?
(ii)What is the probability that I get 6 bad eggs?
d) What is the probability that I get at least 34 good eggs in a week?
Q2. A recent traffic study in the town of Tanunda showed that, on average 300 cars pass through a junction between the hours of 9am to 10am.
a)What is the average number of cars per min?
b)Let X be the number of cars that passs during a one minute period. State the distribution of X and give the mean and this distribution. Now state the probability function of X.
c)Find the probability that no cars pass in a given minute.
d)Find the probability at least two cars pass in two minutes.
e)What is the expected number of cars passing in two minutes?
f)Find the probability that this expected number from part (c) actually pass through a two minute period.