I need help with questions 8 - 10 please with work done please

7. Given that a Binomial Variate X" has a mean of 8 and a variance of - find the values of p. q and n. 8. A window pane is made in the shape of a square whose side length X is a random variable with mean 50 cm and standard deviation 0.1 cm. (a) If P is the perimeter of the pane, find E(P), the mean of P. (b) If A is the area of the pane, find E(A), the mean of A. 9. A factory assembly line producing clocks has a 'defective' rate of one in twenty (i.e. 5% of the clocks produced have faults). (a) For a sample of twenty clocks, find: the expected number of defective clocks; (ii) the probability that the number of defective clocks equals the expected number; (iii) the probability that at least two clocks will be defective. (b) If five separate people take samples of twenty clocks each, what is the probability that all of the five samples will have at least two defective clocks in them? (c) What is the expected number of defective clocks in a day's production of 180? (d) How many clocks would need to be sampled so that there is at least a 50% chance that there would be at least 3 defective clocks in the sample? 10. The number of passengers, X, in vehicles travelling over a bridge has a probability distribution shown below: - for x = 0.1,2,3 p(x) =x+2 0.05 for x = 4,5 (a) Find the value of & and hence find the average number of passengers per vehicle travelling over this bridge. (b) What is the probability that a randomly chosen vehicle has more than the average number of passengers? (c) If 10 vehicles are chosen at random, find the probability (correct to 4 decimal places) that 6 of them have more than the average number of passengers.1. Find the value of a for the following probability distribution: X 2 3 Pr(X = x) 0.1 2a 4a 0.3 Hence find Pr (X'