3)A study shows in a certain school that the average number of hours a student answers his/her module in a day is 10.5 hours with a standard deviation of 1.25. Assuming that the data are normally distributed, a)What is the number of hours in answering modulesof a certain student with a z-score of -2.45? b)Find the probability that the number of hours spent by a student in answering his/her modules is greater than 8 hours. c)Find the probability that the number of hours spent by a student in answering his/her modules is less than 7.5hours d)Find the probability thatthe number of hours spent by a student in answering his/her modules is between 7.5 hours and 12 hours. e)lf there were 1000 students in that school, how many students spent between 7.5 and 12 hours in answering his/her modules
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!
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