Question 6 5. A company of 450 factories. Management is interested in average break downs (X) of productionlines across all 450 factories per month because of the high cost of breakdowns. From historicaldata it was found that there was a mean of 120 breakdowns across all factories with a variance of20. It was also found that about 20% of the factories had no break downs.Answer the following questions.5.1. What does "a mean of 120 break downs" mean?5.2. Give the standard deviation of the population.5.3. Give the variance of the population proportions of the breakdowns.6. Refer to Question 5.6.1 With a month's worth of data, a simple random sample, without replacement, of 60 factorieswas drawn and the following result was determined:X = 100.Explain this in words and in detail.6.2. Find the standard error of the number of breakdowns per month from the sample and interpret6.3. Find the standard error of the proportion of breakdowns per month from the sample.7. Rice Exercise Chapter 7 No 44. Two populations are surveyed with simple random samples. A sample of size #₁is used for population I, which has a population standard deviation o, a sample ofsize n. = 2n1 is used for population II, which has a population standard deviation0₂201. Ignoring finite population corrections, in which of the two sampleswould you expect the estimate of the population mean to be more accurate?Motivate by showing the calculations involved.8. Rice Chapter 7 no 77. Suppose that a simple random sample is used to estimate the proportion of familiesin a certain area that are living below the poverty level. If this proportion is roughly.15, what sample size is necessary so that the standard error of the estimate is .02?The End

Given information: N=450, μ=120, σ2=20, n=60, and x¯=100

5. A company of 450 factories. Management is interested in average break downs (X) of production lines across all 450 factories per month because of the high cost of breakdowns. From historical data it was found that there was a mean of 120 breakdowns across all factories with a variance of 20. It was also found that about 20% of the factories had no break downs. Answer the following questions. 5.1. What does "a mean of 120 break downs" mean? 5.2. Give the standard deviation of the population. 5.3. Give the variance of the population proportions of the breakdowns. 6. Refer to Question 5. 6.1 With a month's worth of data, a simple random sample, without replacement, of 60 factories was drawn and the following result was determined: X = 100. Explain this in words and in detail. 6.2. Find the standard error of the number of breakdowns per month from the sample and interpret it. 6.3. Find the standard error of the proportion of breakdowns per month from the sample.