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1. The following table gives the frequency distribution of the number of hours each group of people out of 40 took to finish the same amount of work. [10 Marks] Number of hours 4-6 7-9 7 10 - 12 12 13 - 15 10 16 - 18 6 n = 40 a) Find the mode, median and mean b) Find the range, variance and standard deviation 2. A random study, on samples, of the number of defective devices produced from two companies produced the following results [10 Marks] Defective Devices Non-defective Total Devices Company A 30 70 100 Company B 60 150 210 Total 90 220 310 a) Give the joint probability table of the produced devices b) What is the probability that a manufactured device is defective? c) What is the probability that a manufactured device is from company B and non-defective? d) What is the probability that a manufactured device is from company A or company B? e) What is the probability that a device is defective if it is manufactured by company B?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 2 3 4 P(x) 0.24 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?6. In high school, the probability of a student being a girl is 0.35. If 50 students are randomly selected, find [10 Marks] a) The probability that more than 27 will be girls b) The probability that more than 20 will not be girls c) The probability that more than 5 but less than 30 students will be girls. 7. Construct 90% confidence intervals to estimate the difference between population means and proportions for the following provided data: [10 Marks] a) Sample 1 Sample 2 * = 65 X2 = 55 57 = 9 $ = 12 n = 19 n2 = 25 i) Assume 01 # 02 ii) Assume 01 = 02 b) Sample 1 Sample 2 X1 = 150 X2 = 100 1 = 300 n2 = 400 8. Suppose, out of a certain population, a sample of size 55 and mean 68 was extracted. By taking a = 0.05, carry out [10 Marks] a) A hypothesis test if the sample mean is different from the population mean of 70 for o = 5. b) A hypothesis test if the sample mean is different from the population mean of 70 for s = 7.9. It is believed that it does not matter where you by your car from, whether from company A or company B, all take the same average time until they are broken down. - A sample of 42 taken from company A showed an average time to breakdown of 12 years with standard deviation of 4 years. - A sample of 51 taken from company B showed an average time to breakdown of 10 years with standard deviation of 6 years. With a = 0.01, test if the belief is true assuming 01 = 02. [10 Marks] 10.A new drug that induces sleeping is developed and the developer claims the drug has the same effect on both children and adults. In trying to find out if the developer's claim is true, we get random samples of 50 children and 90 adults and find that after administering the drug, 23 of children slept and 40 of adults slept. By taking a = 0.1 and interpreting results after testing, carry out [10 Marks] a) A hypothesis test of the developer's claim if it is true