Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 47 minutes and standard deviation 19 minutes. A researcher observed 10 students who entered the library to study. Round all answers to 4 decimal places where possible. A. What is the distribution of XX? XX ~ N(,) B. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) C. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
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!
Suppose that the amount of time that students spend studying in the library in one sitting is
A. What is the distribution of XX? XX ~ N(,)
B. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
C. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
D. If one randomly selected student is timed, find the probability that this student's time will be between 39 and 46 minutes.
E. For the 10 students, find the probability that their average time studying is between 39 and 46 minutes.
F. Find the probability that the randomly selected 10 students will have a total study time more than 520 minutes.
G. For part e) and f), is the assumption of normal necessary? NoYes
h. The top 10% of the total study time for groups of 10 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker? minutes
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