Problem 1: When using the central limit theorem for means with n = 79, it is not necessary to assume the distribution of the population data is normally distributed. O True O False Problem 2: If the sample size is 36 and the population standard deviation is 24, then the standard deviation of the sampling distribution for means is 4. O True O False Problem 3: A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 95.9- cm and a standard deviation of 1.3-cm. For shipment, 48 steel rods are bundled together. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N b. What is the distribution of 2? & - N( C. For a single randomly selected steel rod, find the probability that the length is between 95.8-cm and 96-cm. d. For a bundled of 48 rods, find the probability that the average length is between 95.8-cm and 96-cm. e. For part d), is the assumption of normal necessary? O Yes NoProblem 4 A researcher is interested in finding a 95% confidence interval for the mean number of times per day that college students text. The study included 119 students who averaged 33.1 texts per day. The standard deviation was 22.5 texts. a. To compute the confidence interval use a distribution. b. With 95% confidence the population mean number of texts per day is between and texts . c. If many groups of 119 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population number of texts per day and about percent will not contain the true population mean number of texts per day. Problem 5 You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 409 randomly selected caterpillars observed, 44 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 95% confidence the proportion of all caterpillars that lived to become a butterfly is between and Problem 6 You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately o = 55.7. You would like to be 90% confident that your estimate is within 1 of the true population mean. How large of a sample size is required? Do not round mid-calculation. n = Problem 7 You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 60%. You would like to be 90% confident that your estimate is within 1% of the true population proportion. How large of a sample size is required? Do not round mid- calculation