The company selects 50 samples of coffee every hour from its pro-duction line and determines the caffeine content. From historical data, the caffeine content (in milligrams, mg) is known to have a normal distribution with s^ 5 7.1 m.gDuring a 1-hour time period, the 50 samples yielded a mean caffeine content of y 5 110 mg. a. Identify the population about which inferences can be made from the sample data. b. Calculate a 95% confidence interval for the mean caffeine content m of the coffee produced during the hour in which the 50 samples were selected. c. Explain to the CEO of the company in nonstatistical language the interpretation of the constructed confidence interval.
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!
The company selects 50 samples of coffee every hour from its pro-duction line and determines the caffeine content. From historical data, the caffeine content (in milligrams, mg) is known to have a
a. Identify the population about which inferences can be made from the sample data.
b. Calculate a 95% confidence interval for the mean caffeine content m of the coffee produced during the hour in which the 50 samples were selected.
c. Explain to the CEO of the company in nonstatistical language the interpretation of the constructed confidence interval.
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