A sample of 13 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 3 ounces with a standard deviation of 0.14 ounces. The population standard deviation is known to be 0.1 ounce. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) Find the following. (Round your answers to two decimal places.) (i) x= (ii) σ = (iii) Sx = × Part (b) In words, define the random variable X. the mean weight of the candies the number of candies in a bag the weight, in ounces, of one bag of candy the weight, in ounces, of a piece of candy Part (c) In words, define the random variable X. the mean number of candies for the sample of 13 bags the mean number of candies from each bag that weigh 3 ounces the mean weight, in ounces, of the pieces of candy the mean weight, in ounces, for the sample of 13 bags Part (d) Which distribution should you use for this problem? (Round your answers to three decimal places.) Explain your choice. The Student's t-distribution should be used because the sample size is small. The standard normal distribution should be used because the population standard deviation is known. The Student's f-distribution should be used because the sample standard deviation is given. The standard normal distribution should be used because the sample standard deviation is known. Construct a 90% confidence interval for the population mean weight of the candies. (i) State the confidence interval. (Round your answers to three decimal places.) (ii) Sketch the graph. C.L.= α 82 (iii) Calculate the error bound. (Round your answer to three decimal places.) Part (f) Construct a 98% confidence interval for the population mean weight of the candies. (i) State the confidence interval. (Round your answers to three decimal places.) (ii) Sketch the graph. α C.L.= A 82 (iii) Calculate the error bound. (Round your answer to three decimal places.) X