A new boulangerie in the south of Cologne is known to weigh the baguette (in grams) is normally distributed with an unknown expected value µ and a theoretical one Standard deviation of 5.10 grams for a sample of 16 for examination the average baguette weight has an average weight of 249.54 grams surrender. a) Determine a specific confidence interval for the expected value of the baguette weight at the confidence level 0.97 and enter the length of this interval. b) How large must the sample be at least so that a confidence interval for the expected value of the baguette weight at the confidence level 0.97 has a length of at most 2.5 grams? c) How does the length of the confidence interval from sub-task a) change (with the same sample) if the confidence level is lowered to 0.92?
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!
A new boulangerie in the south of Cologne is known to weigh the baguette
(in grams) is
a) Determine a specific confidence interval for the expected value of the baguette weight at the confidence level 0.97 and enter the length of this interval.
b) How large must the sample be at least so that a confidence interval for the expected value of the baguette weight at the confidence level 0.97 has a length of at most 2.5 grams?
c) How does the length of the confidence interval from sub-task a) change (with the same sample) if the confidence level is lowered to 0.92?
d) It is also known that the weight of baguettes (in grams) from a second boulangerie in the village is also normally distributed, whereby both parameters µ and σ are unknown here.
For this boulangerie, a
surrender. Also determine a specific confidence interval for the expected value the baguette weight of this second boulangerie, here too at a confidence level of 0.97, and interpret the confidence interval obtained.
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