3. If the Manufacturer knows the probability of a manufactured device being defective is 0.30 and she is to manufacture 4 devices, finish the following table provided that X is the number of defective devices [10 Marks] x 0 1 P(x) 0.24 2 3 4 a) What is the probability that at most 2 of the manufactured devices will be defective? b) What is the probability that at least 2 of the manufactured devices will be defective? c) What is the probability that the number of defective devices will be between 1 and 4? d) Calculate E(X) and V(X) using the table and then using the binomial distribution. Compare the results. 4. The life spans of trucks manufactured by company A are normally distributed with a mean of 10 years and variance of 25 years. [10 Marks] a) What is the probability that a random truck bought from company A will have a life span of more than 12 years? b) What is the probability that a random truck bought from company A will have a life span of less than 7 years? c) What is the probability that a truck randomly bought from company A will have a life span of more than 5 years but less than 25 years 5. Suppose out of the population of mean 70 and variance 100 we extracted random samples of size 45 each with mean denoted by X. [10 Marks] a) Determine the mean and standard deviation for X. b) What is the probability that X will be less than 65? c) What is the probability that X will be greater than 72 but less than 75?