Help me with this Problems, please.
19). 2. Two devices work independently. The working time has an exponential distribution with the mean 50 hours and 70 hours, respectively. Find the probability that during 30 hours (a) both devices work; (b) both devices stop working; (c) at least one device works. "/>
Extracted text: 1. A simple random sample of 255 individuals provided 92 responses “Yes". (a) What is the point estimate of the proportion of the population who would provide “Yes" responses? (b) What is the standard error of the proportion? (c) Compute a 99% confidence interval for the population proportion. 2. A sample of 15 items provides a sample standard deviation of 6. Develop the 95% confidence interval of the population standard deviation. 1. A simple random sample of 45 items resulted in a sample mean of 24. The population standard deviation is 5. (a) What is the standard error of the mean? (b) At a 90% probability, what is the margin of error? (c) Provide a 95% confidence interval for the population mean. 2. The following data have been collected from a sample of 9 items from a normal population: 11, 7, 9, 12, 14, 6, 5, 10, 8. (a) Find the point estimate for the population mean. (b) Find the point estimate for the population standard deviation. (c) Develop a 99% confidence interval for the population mean. 3. How large a sample should be used to provide a 95% confidence interval with a margin of error of 4, if the population standard deviation is 18? 1. A lift is designed with a load limit of 800 kg. It claims a capacity of 8 people. If the weights of all people using the lift are normally distributed with a mean of 75 kg and a standard deviation of 10 kg, what is the probability that a group of 8 persons will exceed the load limit? What is the probability that a sample mean weight will be within +5kg of the population mean weight? 2. In the next year what is the probability that of the first 50 babies born, 40% to 60% will be boys? 1. Given that X is a normal random variable with the mean of 15 and standard deviation of 3, compute the following probabilities. (a) P(x < 17),="" (b)="" p(16="">< x="">< 18),="" (c)="" p(13="">< x="">< 16),="" (d)="" p(9="">< x="">< 14),="" (e)="" p(x=""> 19). 2. Two devices work independently. The working time has an exponential distribution with the mean 50 hours and 70 hours, respectively. Find the probability that during 30 hours (a) both devices work; (b) both devices stop working; (c) at least one device works.