1. As quality manager of a firm producing mineral water, you are concerned with the amount of water in the bottle which is measured by its weight. The following data represents the weights of 150 bottles that you supplied in your city. 9.17 9.25 9.70 9.58 9.34 9.97 10.36 10.24 9.29 10.74 10.28 10.14 10.77 10.85 10.64 10.31 10.73 9.26 9.24 10.64 10.47 10.59 10.49 9.80 10.76 10.48 9.43 9.78 9.39 10.18 10.43 9.61 10.53 9.68 10.28 10.96 10.89 10.21 10.35 10.23 9.92 10.88 9.44 10.56 10.84 9.44 9.91 10.36 10.60 10.23 10.15 10.91 10.63 9.31 9.53 9.31 9.86 9.25 9.64 10.60 10.67 10.78 10.27 9.23 9.57 10.41 9.37 10.89 9.26 9.70 10.44 9.37 10.44 9.77 10.70 10.02 9.76 9.34 10.63 9.82 9.45 10.90 10.02 9.74 10.97 10.72 10.61 9.08 9.50 10.45 9.19 9.46 9.75 10.53 9.09 9.10 9.78 9.27 9.19 10.67 9.29 10.76 9.36 9.87 10.13 10.52 10.63 10.18 9.81 10.87 9.26 9.48 9.58 9.67 10.23 9.96 10.08 10.33 10.49 9.45 9.60 9.43 10.59 9.81 10.83 10.07 9.77 9.10 9.15 9.01 10.13 9.45 9.92 10.13 9.70 10.19 10.08 9.77 10.67 10.80 10.89 9.40 9.42 9.75 10.07 9.58 10.73 10.09 9.96 10.18 9.11 10.96 9.73 10.81 10.57 10.49 10.87 10.06 10.62 9.39 a. You select a random sample of 5 (sequential selection is not allowed) and calculate the interval estimate of the mean weights population standard deviation as 0.6. (Please mention the data points of the sample that you have selected, if you fail to do so your submission will not be evaluated) b. You found out that the standard deviation of the population is incorrect. So now you should rely on the sample standard deviation. Find the new interval estimate of the mean weights of the bottles at 95% confidence considering of the bottles at 95% confidence considering the same sample as you chose in (a).
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Step by step
Solved in 3 steps with 1 images