Page 2 of 6 A study of the growth of a certain kind of orchid showed that (under controlled conditions) a random sample of 40 of these orchids grew on the average, x = 32.5 mm year mm Given that s = 3.2 year ", construct a 99% confidence interval for the true mean annual growth of this kind of orchid.To test the durability of a new paint for white center lines, a highway department painted test strips across heavily traveled roads in eight different locations, and electronic counters showed that they deteriorated after having been crossed by (data in units x 1000): 143 168 137 108 126 134 162 150 The population data for paint duration are normally distributed. a ) Why can we assume that the sampling distribution of the mean is normal even though the sample size is only 8? b) Construct a 95% confidence interval for the average amount of traffic (vehicles) the new white paint can withstand before it deteriorates. You may use your calculator to calculate the mean and standard deviation or use the formulas given E X = 1128 and E X2 = 161 682.A cereal manufacturer wants to test the performance of one of its filling machines. The machine is designed to discharge a mean amount of u = 340 grams per box, and the manufacturer wants to detect any departure from this setting. This quality study calls for a random sampling of 100 boxes from today's production run and determining whether the mean fill for the run is 340 g/box. The sample yields the following results: n = 100 observations and x = 337.9 g/box. The population standard deviation is known to be o = 14.2 g/box from previous performance tests. The daily production run is N = 2500 boxes. Use these data to conduct the test of hypothesis. Let a = 0.02. Follow the procedure for tests of hypothesis and use a 2% level of significance. Use the following hypotheses ... Ho: M = 340 g/box H1: u # 340 g/boxBy measuring the amount of time it takes a component of a product to move from one workstation to the next, a technologist has estimated that the standard deviation is 5.00 seconds. What sample size should be used in order to be 95% certain that the mean transfer is estimated to within +1.00 seconds